| CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES |
| |
| 作者姓名： | AN Runling HOU Jinchuan |
| |
| 作者单位： | AN RUNLING HOU JINCHUAN Department of Mathematics，Shanxi University，Taiyuan 030000，China. Department of Mathematics，Shanxi Teachers University，Linfen 041004，Shanxi，China. |
| |
| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10471082)
the Shanxi Provincial Natural Science Foundation of China (No.20021005). |
| |
| 摘 要： | Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB B A) =φ(A)φ(5) φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU for all A or φ(A) = cUA U for all A; φsatisfies φ(AB A) = φ(A)φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA V for all A, where A denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U U = c-1I and V V = cI for some nonzero real number c.
|
| 关 键 词： | 模糊乘积空间 自同构 Jordan乘积 乘法映射 |
| 收稿时间： | 5/4/2008 12:00:00 AM |
CHARACTERIZATIONS OF JORDAN $\dag$-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES |
| |
| AN Runling,HOU Jinchuan.CHARACTERIZATIONS OF JORDAN $\dag$-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES[J].Chinese Annals of Mathematics,Series B,2005,26(4):569-582. |
| |
| Authors: | AN Runling and HOU Jinchuan |
| |
| Institution: | [1]Department of Mathematics, Shanxi University, Taiyuan 030000, China. [2]Department of Mathematics, Shanxi Teachers University, Linfen 041004, Shanxi, China. |
| |
| Abstract: | Let H and K be indefinite inner product spaces. This paper shows that a bijective map Φ: B(H) → B(K) satisfies Φ(AB+ + B+A) = Φ(A)Φ(B)+ + Φ(B)+Φ(A) for every pair A,B ∈ B(H) if and only if either Φ(A) = cUAU+ for all A or Φ(A) = cUA+U+ for all A; Φ satisfies Φ(AB+A) = Φ(A)Φ(B)+Φ(A) for every pair A, B ∈ B(H) if and only if either Φ(A) = UAV for all A or Φ(A) = UA+V for all A, where A+ denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U+U = c-1I and V+V = cI for some nonzero real number c. |
| |
| Keywords: | Indefinite inner product spaces (?)-Automorphisms Jordan product |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文 |
