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2021年广州大学算子理论与算子代数学术交流会

时间:2021-07-26 点击数:

报告题目与摘要


报告人:鲍官龙

题 目:Mobius invariant function spaces and the range of the Cesaro operator acting on $H^\infty$

报告摘要:In this talk, we first consider Mobius invariant function spaces generated by Dirichlet spaces with a class of superharmonic weights that are Green’s potentials of positive Borel measures on the unit disk. Then we investigate the relation between these Mobius invariant function spaces and the range of the Cesaro operator acting on $H^\infty$. Our conclusion refines some previous results in the literature.


报告人:曹怀信

题 目:量子信息掩盖

报告摘要:量子信息掩盖是指将编码在量子态中的信息映射到一个复合系统中使得所有子系统上的观测者都无法获得原有信息的任何知识。这一概念是由Modi等人在文献[Phys. Rev. Lett. 120, 230501 (2018)]中提出并研究的. 后来,费少明教授、范桁教授、李波教授、Xiao-Bin Liang、李茂生博士后及王艳玲博士等学者对相关问题进行了深入细致的研究,得到了非常漂亮的结果。本报告在介绍相关概念的基础上,介绍一组纯态可以被一个算子掩盖的充分必要条件,进而给出一个无法被掩盖的四态集合,这意味着要掩盖任意未知纯态是不可能的(no-making theorem)。 其次,构造一个掩盖器(masker)并且得到它的最大可掩盖集,进而给出Modi论文中提出的一个猜想的肯定答案。最后,提出混合态掩盖问题,证明混合态的一个可交换子集能够被一个等距算子掩盖。通过建立多体掩盖的充分必要条件,得到量子多体掩盖与量子纠错码的一个等价关系。


报告人:曹小红

题 目:Property (R) for functions of operators and its perturbations

报告摘要:Let $H$ be a complex separable infinite dimensional Hilbert space and $B(H)$ be the algebra of all bounded linear operators on $H$. $T \in B(H)$ is said to satisfy property (R) if $\sigma_{a}(T) \setminus \sigma_{ab}(T)=\pi_{00}(T)$, where $\sigma_{a}(T)$ and $\sigma_{ab}(T)$ denote the approximate point spectrum and the Browder essential approximate point spectrum of $T$ respectively, and $\pi_{00}(T)={\lambda \in iso \sigma(T):0<dim N(T-\lambda I)<\infty}$. In this paper, using a new spectrum we talk about the property (R) for functions of operators as well as its stability.


报告人:陈泳

题 目:Ranks of commutators for some classes of truncated Toeplitz operators

报告摘要:In this talk, we describe the kernels and ranks of commutators of truncated Toeplitz operator with symbols induced by certain inner functions. Our results generalize some recent results to infinite dimensional model spaces.


报告人:程国正

题 目:Random Dirichlet Multipliers and Littlewood-type Theorems

报告摘要:In this talk, we consider the classical Littlewood's theorem on Dirichlet spaces $\mathcal{D}^p$. In detail, let $$(\mathcal{R}f)(z)=\sum_{n=0}^{\infty}\pm a_nz^n,\quad f(z)=\sum_{n=0}^{\infty}a_nz^n\in H(\mathbb{D}).$$ Firstly, we characterize the symbol spaces $\{f\in H(\mathbb{D}):\mathbb{P}\{\mathcal{R}f\in \mathcal{M}^p\}=1\}$ and $\{f\in H(\mathbb{D}):\mathbb{P}\{\mathcal{R}f\in \mathcal{D}^p\}=1\},$ where $\mathcal{M}^p$ is the multiplier algebra of $\mathcal{D}^p.$ Moreover, we completely solve a Littlewood-type problem $\mathcal{R}: \mathcal{D}^p\rightarrow \mathcal{M}^q.$


报告人:邓春源

题 目:On the properties of operator parallel sum

报告摘要:We extend the operations of parallel sum and parallel subtraction from the cone of bounded nonnegative self-adjoint operators to the linear bounded operators on a Hilbert space. The basic properties of the parallel sum and subtraction were developed for nonnegative matrices in finite-dimensional spaces. In this talk, generalization to non-selfadjoint operators is considered and various properties of parallel sum and subtraction are given. The common upper and lower bounds of positive operators by using the parallel sum are given. Moreover, some relationships between the parallel addition and subtraction of projections are obtained.


报告人:方小春

题 目:大子代数和广义迹逼近

报告摘要:我们引入了一类广义的迹逼近C*-代数, 这类广义的迹逼近C*-代数是Phillips的中心大子代数和Lin的迹逼近C*-代数的推广。Niu提出的满足某些性质得到的交叉积C*-代数在我们提出的这类广义的迹逼近C*-代数中,然而这些交叉积C*-代数既没有一个中心大子代数也不在迹逼近C*-代数类中。我们讨论了迹逼近C*-代数的遗传性质,即:如果F是一类具有某种性质的C*-代数,通过F中的C*-代数广义迹逼近之后得到C*-代数也就有这种性质。


报告人:房军生

题 目:Sums of projections in semifinite factors

报告摘要:Which positive operators in a factor von Neumann algebra can be written as sums of projections? This question is studied by Victor Kaftal, Ping Wong Ng, and Shuang Zhang. They obtained beautiful results on the question. In this talk we report some new progress on the question. This is joint work with Xinyan Cao and Zhaolin Yao.


报告人:郭坤宇

题 目:The theory of $H^p$-spaces in infinitely many variables and Fatou’s theorem

报告摘要:This is a lecture on function spaces $H^p$ in infinitely many variables. We first summarize some basic conclusions in finitely many variables, and then pass to the case of infinitely many variables. We particularly highlight the role of Fatou’s theorem in $H^p$-spaces. Some results in this lecture are new, and some previously known results are reproved by some different methods.


报告人:郭志华

题 目:Conversions between quantum resources by means of incoherent operations

报告摘要:One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. Quantum coherence and quantum correlation are two fundamental resources in quantum information and computation. In this work, we first focus on the question of creating quantum correlation from a coherent state via incoherent quantum operations. We give the specific forms of states in two-qubit systems, called super-coherent ones, that can be mapped to quantum correlated ones via some genuinely incoherent operation. We find that there exist some coherent states that are not super-coherent. Furthermore, we prove that a state can be mapped to a quantum correlated state via an incoherent operation if and only if it is coherent. Second, we ask if coherence, already present in a reference system, can be broadcast to the auxiliary system via incoherent operations. We prove that it is impossible for a weaker form of broadcasting via incoherent operations. This shows that broadcasting of coherence is forbidden via incoherent operations in every finite-dimensional system. We also prove that a generalized form of broadcasting via incoherent quantum operations can occur if and only if the state of system is coherent. In this case, we are able to give a method for constructing an incoherent quantum operation to generalized broadcast coherence.


报告人:侯成军

题 目:Continuous orbit equivalence based on equivalence relations

报告摘要:In this talk, we consider continuous orbit equivalence and strong (respective, weak) continuous orbit equivalence for automorphism systems of \'{e}tale equivalence relations, and characterize them in terms of the semi-direct product groupoids, as well as their reduced groupoid $C^*$-algebras with canonical Cartan subalgebras.


报告人:侯晋川

题 目:A computable multipartite multimode Gaussian correlation measure and the monogamy relation for continuous-variable systems

报告摘要:A computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$-partite continuous-variable (CV) systems with $k\geq 2$. ${\mathcal M}^{(k)}$ depends only on the covariance matrix of CV states, is invariant under any permutationof subsystems, is a quantification without ancilla problem, nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite local Gaussian unitary operations), vanishes on $k$-partite product states. For a $k$-partite Gaussian state $\rho$, ${\mathcal M}^{(k)}(\rho)=0$ if and only if $\rho$ is a $k$-partite product state. Moreover, ${\mathcal M}^{(k)}$ satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. ${\mathcal M}^{(k)}$ is not bipartite like monogamous, but, ${\mathcal M}^{(k)}$ is complete monogamous and tight complete monogamous.


报告人:侯绳照

题 目:Fock型空间上的积分算子



报告人:胡璋剑

题 目:IDA and Hankel operators on Fock spaces

报告摘要:We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite. By using IDA and $\overline \partial$-estimates, we characterize boundedness, compactness and Schatten $p$-class membership of Hankel operators on weighted Fock spaces in $\C^n$. As an application, for bounded symbols, we show that the Hankel operator $H_f$ is compact (or of Schatten $p$-class) if and only if $H_{\bar f}$ is compact (or of Schatten $p$-class resp.), which complements the classical compactness result of Berger and Coburn. We also apply our results to the Berezin-Toeplitz quantization and answer a related question of Bauer and Coburn.


报告人:黄寒松

题 目:待更新

报告摘要:待更新


报告人:吉国兴

题 目:Noncommutative $H^p$ spaces associated with type 1 subdiagonal algebras

报告摘要:In this talk, we discuss noncommutative $H^p$ spaces associated with type 1 subdiagonal algebras. Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We consider a Riesz type factorization theorem in noncommutative $H^p$ spaces associated with $\mathfrak A$. It is shown that if $1\leq r,p,q<\infty$ such that $\frac1r=\frac1p+\frac1q$, then for any $h\in H^r$, there exist $h_p\in H^p$ and $h_q\in H^q$ such that $h=h_ph_q$. Beurling type invariant subspace theorem for noncommutative $L^p(1< p<\infty)$ space is obtained. Furthermore, we show that a $\sigma$-weakly closed subalgebra containing $\mathfrak A$ of $\mathcal M$ is also a type 1 subdiagonal algebra. As an application, We prove that the relative invariant subspace lattice $Lat_{\mathcal M}\mathfrak A$ of $\mathfrak A$ in $\mathcal M$ is commutative.


报告人:纪奎

题 目:On the unitarily equivalence of Cowen-Douglas operators

报告摘要:In this talk, we will recall some results on the unitarily equivalence of Cowen-Douglas operators, with a particular focus on unitarily equivalence of Cowen-Douglas operators in terms of the connections of related Hermitian Holomorphic vector bundles.


报告人:蒋春澜

题 目:Geometric invariants of operators

报告摘要:In this report,we will show that curvature;the second fundamental form;chern polynomials are similarity invaiants of a class of Cowen-Douglas operators,and positive answering two open questions raised by R.Douglas.In addition,we will also show some application of the above results.


报告人:李磊

题 目:Maps preserving the means

报告摘要:I will consider maps preserving different means in the positive definite cone of C*-algebras and show that such maps can extend to be Jordan *-isomorphisms. In the commutative cases, I will give the representation of such maps.


报告人:李颂孝

题 目:Difference of Composition operators on some analytic function spaces

报告摘要:In this talk, we discuss the boundedness, compactness of composition operators on some analytic function spaces in the unit disk.


报告人:李玉成

题 目:On the properties of canonical solution operator to $\bar{\partial}$ restricted to Dirichlet space

报告摘要:In this talk, we first show that the canonical solution operator $S_1$ to $\bar{\partial}$ restricted to (0,1)-forms with holomorphic function coefficients can be expressed by an integral operator using the Dirichlet kernel. Then we prove that operator $S_k\,(k\geq 1)$ is a Hilbert-Schmidt operator on the Dirichlet space of $\mathbb{D}$, but fails to be the Hilbert-Schmidt operator on the Dirichlet space of $\mathbb{D}^{2}$. Finally we show that the concomitant operator $P_{k}$ of $S_{k}\,(k\geq 2)$ is similar to the direct sum of $k$ copies of the concomitant operator $P_{1}$ of $S_{1}$.


报告人:李智强

题 目:Dynamic Pressure for Differential Operators associated to Partially Hyperbolic Diffeomorphisms

报告摘要:In this talk, we exhibit a calculation of dynamical pressure for PHDs (Partially Hyperbolic Diffeomorphisms) with respect to sub-additive potentials. This is a joint work with Wenda Zhang and Yunhua Zhou.


报告人:梁玉霞

题 目:Nearly invariant subspaces for shift operator

报告摘要:For a shift operator $T$ with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly $T^{-1}$ invariant subspaces in Hilbert space in terms of invariant subspaces under the backward shift. Going further, given any finite Blaschke product $B$, we give a description of the nearly $T_{B}^{-1}$ invariant subspaces for the operator $T_B$ of multiplication by $B$ in a scale of Dirichlet-type spaces.


报告人:刘磊

题 目:Projection Toeplitz operator on the Bergman space

报告摘要:In this talk we mainly consider when the Toeplitz operator is a projection on the Bergman space and when the product of two Toeplitz operators is a projection on the Bergman space.


报告人:刘锐

题 目:A toolkit for constructing dilations of frame decompositions and (non-commutative) operator-valued measures on Banach spaces

报告摘要:Dilation theory is a paradigm for studying operators by way of exhibiting operators as the compression of operators which are in some sense well behaved. In this talk, we introduce a general dilation theory from frame decompositions and operator-valued measures (OVMs) on (reflexive) Banach spaces to the non-commutative cases on projection lattices of vN-algebras and operator algebras on Banach spaces. We construct the minimal dilation for quantum OVMs from projection lattices of finite vN-algebras without type $I_2$ direct summand to B(X) where the Banach space X is the sequence spaces $l^p (p<2)$ or has Shur property. As a corollary, we get the corresponding Jordan dilation. By non-commutative projection-partition tree technique, we obtain the dilation for quantum OVMs with bounded p-variation, which have natural examples on completely bounded maps and non-commutative $L^p$ spaces (p>2).


报告人:刘小松

题 目:Embedding derivatives and Area operators of Hardy spaces into Lebesgue spaces in the unit ball of $\mathbb{C}^n$

报告摘要:We characterize the compactness of embedding derivatives from Hardy space $H^p$ into Lebesgue space $L^q(\mu)$. We also characterize the boundedness and compactness of area operators from $H^p$ into $L^q(\mathbb{S}_n)$. Some of the tools used in the proof of the one dimensional case are not available in higher dimensions, such as the strong factorization of Hardy spaces. Therefore, we need the theory of tent spaces which was established by Coifman, Mayer and Stein in 1985. This joint work with Zengjian Lou and Ruhan Zhao.


报告人:卢玉峰

题 目:待更新

报告摘要:待更新


报告人:吕小芬

题 目:Tent spaces and related operators

报告摘要:In this talk, we give the characterizations on area integral operators from p-th Hardy spaces (or Bergman spaces) to q-th Lebesgue spaces. Meanwhile, the embedding theorems from Hardy spaces (or Bergman spaces) into tent spaces are obtained.


报告人:马攀

题 目:On similarity and commutant of analytic Toeplitz operators on the Dirichlet space

报告摘要:In this talk, we will present some progress on similarity and commutant of analytic Toeplitz operators on the Dirichlet space. This talk is based on a joint work with Professor Yucheng Li.


报告人:齐霄霏

题 目:Nonlocal correlations in the tree network configuration

报告摘要:The process of entanglement swapping showed that suitable measurements can generate nonlocal correlations even from particles that never interacted directly. This fact was generalized to the concept of bilocality for quantum network, where there are three observers sharing two independent sources. Since then, the nonlocality nature was explored in various quantum networks. In this work, we consider the nonlocality of (2n-1)-partite tree tensor networks, which are widely used in quantum communications. We derive the Bell type inequalities which are respectively satisfied by all (2n-2)-local correlations and all local correlations, and demonstrate the maximal quantum violations of these inequalities and the robustness to noise in these tree-network.


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报告人:乔雨

题 目:Spectra of Georgescu's Algebras associated to N-Body Type Hamiltonians

报告摘要:Let X be a finite-dimensional real vector space, and S a semi-lattice of subspaces of X. Consider Hamiltonians of the form H:=-\Delta+ V, where V is the sum of functions belonging to a special class of functions on X. In order to compute the essential spectrum of H, Georgescu and Nistor introduced a C*-algebra E(X) in 2017. Later on, Mougel, Nistor, and Prudhon defined the C*-algebra E_S(X). However, in the framework of true N-body problems, one naturally considers the Georgescu's C*-algebra G_S(X). We will discuss the relation between these two C*-algebras. It is joint work in progress with Jeremy Mougel and Yunfei Song.


报告人:王凯

题 目:Gaussian limit for determinantal point processes with J-Hermitian kernels

报告摘要:We show that the central limit theorem for linear statistics over determinantal point processes with J-Hermitian kernels holds under fairly general conditions. This is the joint work with Zhaofeng Lin and Yanqi Qiu.


报告人:王利广

题 目:On preservers related to the spectral geometric mean and Heron mean

报告摘要:Means play an important role in matrix theory and operator theory. The preserver of means is an active research field. In this talk, I will talk about the preserver transformations between positive definite cones in operator algebras relating the spectral geometric mean of Fiedler and Ptak. We also discuss kinds of structural similarities and dissimilarities between the Kubo-Ando geometric mean and the spectral geometric mean. We will also consider preservers related to Heron means. This talk is based on joint work with Xiujiao Chi, Kaixuan Li, Lei Li and Lajos Molnar.


报告人:王茂发

题 目:Linear combinations of composition operators on a Hilbert space of Dirichlet series

报告摘要:The aim of this talk is to characterize when linear combinations of composition operators are compact on the Hilbert space of Dirichlet series with square summable coefficients. Especially, we discuss the topological structure of the set of composition operators acting on the Hilbert space of Dirichlet series. It reveals that there exists a continuous arc in the set of all bounded composition operators on the space containing non-compact ones. Moreover, it is shown that the linear combinations of composition operators induced by finitely many distinct linear symbols are compact only when each one of them is compact. This is a joint work with Frederic Bayart and Xingxing Yao.


报告人:王勤

题 目:Relative expander graphs and the coarse Baum-Connes conjecture

报告摘要:Expander graphs are highly connected and sparse graphs, which do not coarsely embed into Hilbert space, and are sources for counterexamples to the coarse Baum-Connes conjecture. Recently, G. Arzhantseva and R. Tessera introduce a notion of relative expander to give the first example of sequences of finite Cayley graphs of uniformly bounded degree, and even an example of finitely generated group, which do not coarsely embed into any Lp-spaces for any p>1, yet do not contain any genuine expander. We show that the coarse Baum-Connes conjecture holds for all these relative expander graphs and finitely generated groups. This is joint work with Jintao Deng (University of Waterloo) and Guoliang Yu (TAMU).


报告人:王子鹏

题 目:The metric projections onto closed convex cones in a Hilbert space

报告摘要:We study the metric projections of a vector onto the closed convex cone in a real Hilbert space $\mathscr{H}$ generated by a sequence $\mathcal{V} = \{v_n\}_{n=0}^\infty$. As applications of our main results, we obtain the best approximations of many concrete functions in $L^2([-1,1])$ by polynomials with non-negative coefficients. This is based on a joint work with QIU Yanqi.


报告人:吴文明

题 目:幂等元集合上的L^2-等距映射

报告摘要:我们将首先回顾和总结Wigner定理的历史和进展,然后介绍幂等元集合上的L^2-等距映射的刻画。


报告人:徐宪民

题 目:An introduction to the Invariant Subspace Problem—–a approach via composition operators

报告摘要:In this talk, we introduce the approach attacking the Invariant Subspace Problem(ISP)

via composition operators. The result of Nordgren,Rossenthal and Wintrobe shown that ,for a

hyperbolic automorphism $\varphi$ of the unit disk $\mathbb{D}$, the ISP has a positive solution if and only if every minimal non-trivial invariant subspace of $C_{\varphi}$ on $H^{2}(\mathbb{D})$ is one dimensional. Recently, Carm and Noor complete the old solution and generalize it to the case for general linear fractional self-map of $\mathbb{D}$. Thus we can attack the ISP by studying a simple composition operator $C_{\varphi_{a}}$ on the Hardy space $H^{2}(\mathbb{D})$, where $\varphi_{a}(z)=az+(1-a)$ with $a\in (0,1)$.


报告人:晏福刚

题 目:Discrete Hilbert transform and its truncation on function spaces

报告摘要:In this talk, we will give a norm estimation of discrete Hilbert transform on Hardy spaces. we shall also discuss the boundedness of discrete Hilbert transform on Bergman spaces.


报告人:赵显锋

题 目:Toeplitz algebras on Fock spaces

报告摘要:We discuss Toeplitz algebras generated by certain class of Toeplitz operators on the $p$-Fock space with $1<p<\infty$. Let BUC($\mathbb C^n$) denote the collection of bounded uniformly continuous functions on $\mathbb C^n$. We show that the Toeplitz algebra which has a translation invariant closed subalgebra of BUC($\mathbb C^n$) as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols. This answers a question recently posed by R. Fulsche.


报告人:周泽华

题 目:Some results for the spectra of weighted composition operators

报告摘要:In this talk we will give some results about the spectra of weighted composition operators.


报告人:朱森

题 目:Toeplitz operators on random Hardy spaces

报告摘要:We initiate to study a random counterpart of Toeplitz operators on the classical Hardy space $H^2$. Using a sequence $\{X_n: n=0,\pm1,\pm2,\cdots\}$ of i.i.d., positive random variables with law $\mu$, we introduce random Hilbert spaces $L^2_\mu$ and $H^2_\mu$, which are random counterparts of classical $L^2$ and $H^2$ over the unit circle. Toeplitz operators on $H^2_\mu$ are compressions of multiplication operators on $L^2_\mu$ to $H^2_\mu$. We shall discuss some results concerning the spectral theory of Toeplitz operators on $H^2_\mu$.




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