컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0506 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Algebra / Representation Theory / Lie Theory (SS-02) |
| 영문제목 (Title(Eng.)) |
Additive preservers of tensor product of rank one Hermitian matrices |
| 저자(Author(s)) |
Ming-Huat Lim1 Institute of Mathematical Sciences, University of Malaya1 |
| 초록본문(Abstract) | Let $K$ be a field of characteristic not two or three with an involution and $F$ be its fixed field. Let $H_m$ be the $F$-vector space of all $m$-square Hermitian matrices over $K$. Let $\rho_m$ denote the set of all rank-one matrices in $H_m$. In the tensor product space $\otimes_{i=1}^kH_{m_i}$, let $\otimes_{i=1}^k\rho_{m_i}$ denote the set of all decomposable elements $\otimes_{i=1}^kA_i$ such that $A_i\in\rho_{m_i}$ for $i=1,\cdots,k$. We characterize additive maps $T$ from $H_m\otimes H_n$ to $H_s\otimes H_t$ such that $T\left(\rho_m\otimes\rho_n\right)\subseteq\left(\rho_s\otimes\rho_t\right)\cup\{0\}$, from which we obtain a characterization of linear maps between tensor products of two real vector spaces of complex Hermitian matrices that send separable pure states to separable pure states. We also classify almost surjective additive maps $L$ from $\otimes_{i=1}^kH_{m_i}$ to $\otimes_{i=1}^lH_{n_i}$ such that $L\left(\otimes_{i=1}^k\rho_{m_i}\right)\subseteq\otimes_{i=1}^l\rho_{n_i}$, where $2\le k\le l$. When $K=F$ and is algebraically closed, we show that every linear map on $\otimes_{i=1}^kH_{m_i}$ that preserves $\otimes_{i=1}^k\rho_{m_i}$ is induced by $k$ bijective linear rank-one preservers on $H_{m_i}$ for $i=1,\cdots,k$. |
| 분류기호 (MSC number(s)) |
15A03, 15A69, 15A86 |
| 키워드(Keyword(s)) | Hermitian matrix, rank one preserver, additive map, tensor product |
| 강연 형태 (Language of Session (Talk)) |
English |