Organizer: Jianlian Cui
July 14, 2013
Room A-304,ScienceBuilding
Schedule:
9.00-10.00am
Chi-kwong Li (CollegeofWilliamandMary,USA)
Title:Jordanproducts and preserver problems
Abstract：We discuss results and problems onJordanproducts of operators, and related preserver problems.
10.00-11.00am
Nagi-ching Wong（National Sun Yat-sen University）
Title:Zero products and norm preserving orthogonally additive homogeneous polynomials on C*-algebras
Abstract:Let P:A\to B be a bounded orthogonally additive and zero product preserving $n$-homogeneous polynomial between C*-algebras. We show that, in the commutative case that A=C_0(X) and B=C_0(Y), there exist a bounded continuous function h in C(Y) and a map \varphi: Y\to X such that Pf=h\cdot (f\circ\varphi)^n. In the general case, we show that there is a central invertible multiplier h of B and a surjectiveJordanhomomorphism J: A\to B such that Pa = hJ(a)^n, provided that P(A)\supseteq B^+. Similar Banach-Stone type theorems also hold for orthogonally additive n-homogeneous polynomials which are n-isometries. We also discuss the structure of orthogonally additive and zero product preserving holomorphic functions on commutative C*-algebras.
11.00-12.00am
Raymond Sze (TheHong KongPolytechnicUniversity)
Title:Preserver problems arising in quantum information science
Abstract:The study of linear preserver problems has a long history in matrix and operator theory. It concerns the characterization of linear maps on matrices or operators with special properties. Recently, researchers are interested in linear preserver problems that are related to quantum information science. In this talk, some recent developments of this topic will be discussed.
2.30-3.30pm
Jinchuan Hou (TaiyuanUniversityof Technology)
Title:Lie ring isomorphisms between nest algebras on Banach spaces
Abstract:Let N and M be nests on Banach spaces X and Y over the (real or complex) field F and let Alg N and Alg M be the associated nest algebras, respectively. It is shown that a map \Phi: Alg N\rightarrow Alg M is a Lie ring isomorphism (i.e., \Phi is additive, Lie multiplicative and bijective) if and only if \Phi has the form \Phi(A) = TAT^{-1} + h(A)I for all A in Alg N or \Phi(A)=-TA^*T^{-1}+h(A)I for all A in Alg N, where h is an additive functional vanishing on all commutators and T is an invertible bounded linear or conjugate linear operator when \dim X=\infty; T is a bijective \tau-linear transformation for some field automorphism \tau of F when \dim X
3:30-4:00 pm, Tea Break
4.00-5.00pm
Yiu-tung Poon (Iowa State University,USA)
Title:Linear maps preserving the higher numerical ranges of tensor product of matrices
Abstract:For a positive integer n, let M_n be the set of n \times n complex matrices. Suppose m,n\ge 2 are positive integers and k\in \{1,\ldots, mn-1\}. Denote by W_k(X) the k-numerical range of a matrix X\in M_{mn}. It is shown that a linear map \phi: M_{mn}\rightarrow M_{mn} satisfies W_k(\phi(A\otimes B)) = W_k(A\otimes B) for all A \in M_m and B \in M_n if and only if there is a unitary U in M_{mn} such that one of the following holds. For all A\in M_m, B\in M_n, \phi(A\otimes B)=U(\varphi(A\otimes B))U^*. mn = 2k and for all A\in M_m, B\in M_n, \phi(A\otimes B)=(\tr(A\otimes B)/k)I_{mn}-U(\varphi(A\otimes B))U^*, where (1) \varphi is the identity map A \otimes B \mapsto A\otimes B or the transposition map A\otimes B \mapsto (A\otimes B)^t, or (2) \min\{m,n\} \le 2 and \varphi has the form A \otimes B \mapsto A \otimes B^t or A \otimes B \mapsto A^t \otimes B.
5.00-6.00pm
Yu Guo (TaiyuanUniversityof Technology)
Title:Concurrence for infinite-dimensional quantum systems
Abstract:Concurrence is an important entanglement measure for states in finite-dimensional quantum systems that was explored intensively inthe last decade. In this paper, we extend the concept of concurrenceto infinite-dimensional bipartite systems and show that it iscontinuous and does not increase under local operation and classicalcommunication (LOCC).
You are cordially invited to participate. Thank you very much for your attention.
