数学科学系

Department of Mathematical Sciences

**Organizer: Jianlian Cui**

**July 14, 2013**

** Room A-304, **

**Schedule:**

**9.00-10.00am**

**Chi-kwong Li ( College of William and **

**Title: **

**Abstract****：**We discuss results and problems on

**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 surjective

**11.00-12.00am**

**Raymond Sze (The **

**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 (**

**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<\infty.

**3:30-4:00 pm, Tea Break**

**4.00-5.00pm**

**Yiu-tung Poon (**

**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 (**

**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 in

**You are cordially invited to participate. Thank you very much for your attention.**