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发布日期 : 2021-06-25 浏览次数 :

1. 蒋春澜教授, 河北师范大学

报告题目:Geometric invariants of operators

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.



2. 侯晋川教授,太原理工大学

报告题目:A computable multipartite multimode Gaussian correlation measure

and the monogamy relation for continuous-variable systems

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.



3. 吉国兴教授 陕西师范大学

报告题目:Noncommutative $H^p$ spaces associated with type 1 subdiagonal algebras

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.



4. 纪友清教授,吉林大学

报告题目:The Power Set of Quasinilpotent Weighted Shifts




5. 丁宣浩教授,重庆工商大学

报告题目: The commutant and invariant subspaces for dual truncated Toeplitz operators

摘要:Dual truncated Toeplitz operators on the orthogonal complement of the model space ? with u nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of in . In this paper, we give a complete characterization of the commutant of dual truncated Toeplitz operator , and we even obtain the commutant of all dual truncated Toeplitz operators with bounded analytic symbols. Moreover, we describe the nontrival invariant subspaces of .



6. 吴志强教授,南开大学

报告题目:Ortho-sets and Gelfand spectra

摘要:Motivated by quantum states with zero transition probability, we introduce the notion of ortho-set which is a set equipped with a relation $\neq_\mathrm{q}$ satisfying: $x\neq_\mathrm{q} y$ implies both $x\neq y$ and $y \neq_\mathrm{q} x$.

For an ortho-set, a canonical complete ortholattice is constructed. Conversely, every complete ortholattice comes from an ortho-set in this way. Hence, the theory of ortho-sets captures almost everything about quantum logics.

For a quantum system modeled by the self-adjoint part $B_\mathrm{sa}$ of a $C^*$-algebra $B$, we also introduce a ``semi-classical object'' called the Gelfand spectrum. It is the ortho-set, $P(B)$, of pure states of $B$ equipped with an ``ortho-topology'', which is a collection of subsets of $P(B)$, defined via a hull-kernel construction with respects to closed left ideals of $B$.

We establish a generalization of the Gelfand theorem by showing that a bijection between the Gelfand spectra of two quantum systems that preserves the respective ortho-topologies is induced by a Jordan isomorphism between the self-adjoint parts of the underlying $C^*$-algebras (i.e. an isomorphism of the quantum systems), when the underlying $C^*$-algebras satisfy a mild condition.



7. 刘锐教授,南开大学

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

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 lp (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 Lp spaces (p>2).



8. 曹小红教授,陕西师范大学

报告题目:Property (R) for functions of operators and its perturbations




9. 齐霄霏教授,山西大学

报告题目:Nonlocal correlations in the tree tensor network configuration

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 (2^n-1)-partite tree tensor networks, which are widely used in quantum communications. We derive the Bell type inequalities which are respectively satisfied by all (2^n-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.



10. 孟庆副教授 xpj官方网站

报告题目: Property T of crossed products

摘要: In this talk,  the strong property T of the full crossed product is shown to

coincide with that of the reduced one. We give a complete description for the reduced crossed product to have strong property T. We also give a characterization of the amenability of a locally compact group and a characterization of the inner amenability of an ICC group, both in terms of property T of certain reduced crossed products. Moreover, we introduce Hilbert A -module property T and show that the action has property T if and only if the reduced crossed product has Hilbert A -module property T.



11. 房军生教授 河北师范大学

Title: Sums of projections in semifinite factors

Abstract: 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.



12. 石瑞副教授,大连理工大学

报告题目:Title: Reducible operators in von Neumann algebras (part 2)

摘要: In this talk, we recall density of reducible operators in B(H). Then we apply Property Gamma to consider density of reducible operators in type II_1 factors.



13. 李磊副教授, 南开大学

报告题目:Maps on subgroups of C(X)+




14. 麻振华副教授, 河北建筑工程学院


摘要:In this talk, I will talk about the compact operators under Orlicz function, named noncommutative Orlicz sequence space (denoted by S?(H)), where H is a complex, separable Hilbert space. I will show that the space generalizes the Schatten classes Sp(H) and the classical Orlicz sequence space respectively. After getting some relations of trace and norm, I will give some operator inequalities, Holder inequality and some other classical operator inequalities. Also I will give the dual space and reflexivity of S?(H) which generalizes the results of Sp(H). Finally, as an application, that the Toeplitz operator on the Bergman space belongs to some S?(H).



15. 吴常晖博士, xpj官方网站

报告题目:The wandering subspace property of shift operator on the weighted Bergman spaces

摘要: In this talk, we firstly study the wandering subspace property of the shift operator on the $I_{a}$ type zero based invariant subspaces of the weighted Bergman spaces $L_{a}^{2}(dA_{n})(n=0,2)$ via the spectrum of some Toeplitz operators on the Hardy space $H^{2}$. Secondly, we give examples to show that Shimorin's condition for the shift operator fails on the $I_{a}$ type zero based invariant subspaces of the weighted Bergman spaces $L_{a}^{2}(dA_{\alpha})(\alpha>0)$.



16. 羌湘琦博士 扬州大学

报告题目:Asymptotic continuous orbit equivalence for expansive

摘要: In this talk, we introduce notions of asymptotic  continuous orbit equivalence

and (strongly) asymptotic conjugacy for expansive systems, and characterize them in terms of the transformation groupoids, the principal groupoids coming from the local conjugacy relations and the semi-direct product groupoids of the principal groupoids by the canonical group actions, together with their associated reduced groupoid C*-algebras. We also give some generalization to continuous orbit equivalence up to etale equivalence relation.