A Characterization of *-Automorphism on B(H)

被引：12
作者：
An, Run Ling [1 ]
Hou, Jin Chuan [1 ]
机构：
[1] Taiyuan Univ Technol, Dept Appl Math, Taiyuan 030024, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2010年 / 26卷 / 02期
基金：
中国国家自然科学基金;
关键词：
*-isomorphism; standard operator algebras; Lie-skew product; STANDARD OPERATOR-ALGEBRAS; JORDAN; DERIVATIONS; ADDITIVITY; MAPS;
D O I：
10.1007/s10114-010-8634-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let H be a Hilbert space and A be a standard *-subalgebra of B(H). We show that a bijective map Phi : A -> A preserves the Lie-skew product AB-BA* if and only if there is a unitary or conjugate unitary operator U is an element of B( H) such that F( A) = UAU* for all A is an element of A, that is, Phi is a linear *-isomorphism or a conjugate linear *-isomorphism.
引用
收藏
页码：287 / 294
页数：8
相关论文
共 8 条
[1]   Additivity of Jordan multiplicative maps on Jordan operator algebras [J].
An, RL ;
Hou, JC .
TAIWANESE JOURNAL OF MATHEMATICS, 2006, 10 (01) :45-64
[2]  
Bresar M, 2000, PUBL MATH-DEBRECEN, V57, P121
[3]   Additivity of Jordan maps on standard operator algebras [J].
Lu, FY .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 357 :123-131
[4]   WHEN ARE MULTIPLICATIVE MAPPINGS ADDITIVE [J].
MARTINDALE, WS .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 21 (03) :695-+
[5]   A condition for a subspace of B(H) to be an ideal [J].
Molnar, L .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 235 (235) :229-234
[6]  
SEMRL P, 1991, STUD MATH, V97, P157
[7]   JORDAN ASTERISK-DERIVATIONS OF STANDARD OPERATOR-ALGEBRAS [J].
SEMRL, P .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 120 (02) :515-518
[8]  
Semrl P., 1990, Colloq. Math., V59, P241
1