Characterization of generalized Jordan *-left derivations on real nest algebras

被引：5

作者：

Zhu, J ^{[1
]}

Xiong, CP ^{[1
]}

机构：

[1] Hangzhou Dianzi Univ, Dept Math, Hangzhou 310018, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 404卷

基金：

中国国家自然科学基金;

关键词：

real nest algebra; generalized Jordan *-left derivation; *-left preserving kernel-into-range mapping; generalized inner *-left derivation;

D O I：

10.1016/j.laa.2005.02.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be a real nest algebra of B(H), where H is a real and separable Hilbert space. We show that the following conditions are equivalent for a weak topology continuous linear map phi : A -> B (H): (1) phi is a *-left preserving kernel-into-range mapping, i.e., phi(T)(ker(T)) C ran(T*) for any T is an element of A. (2) phi is a generalized *-left inner derivations, i.e., phi(T) = T*A + BT for some A, B is an element of B(H). (3) phi is a generalized Jordan *-left derivations, i.e., phi(T-2) = T*phi(T) + phi(T)T - T*phi(I) T for any T c V. (4) phi is a *-left 1-preserving kernel-into-range mapping, i.e., phi(T)(ker(T)) subset of ran(T*) for any rank one operator T is an element of A. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：325 / 344

页数：20