CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

doi:10.1016/S0252-9602(17)30029-2

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (3): 668-678.doi: 10.1016/S0252-9602(17)30029-2

CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

薛天娇, 安润玲, 侯晋川

Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

收稿日期:2016-02-29 修回日期:2016-08-31 出版日期:2017-06-25 发布日期:2017-06-25
通讯作者: Runling AN E-mail:runlingan@aliyun.com
作者简介:Jinchuan HOU,jinchuanhou@aliyun.com
基金资助:
Supported by National Natural Foundation of China (11001194) and Provincial International Cooperation Project of Shanxi (2014081027-2).

CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

Tianjiao XUE, Runling AN, Jinchuan HOU

Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received:2016-02-29 Revised:2016-08-31 Online:2017-06-25 Published:2017-06-25
Supported by:
Supported by National Natural Foundation of China (11001194) and Provincial International Cooperation Project of Shanxi (2014081027-2).

摘要/Abstract

摘要： Let A be a unital algebra and M be a unital A-bimodule. A linear map δ:A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ◦ B + A ◦ δ(B)=δ(A ◦ B) for any A, B ∈ A, with A ◦ B=P, here A ◦ B=AB + BA is the usual Jordan product. In this article, we show that if A=AlgN is a Hilbert space nest algebra and M=B(H), or A=M=B(X), then, a linear map δ:A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

关键词: Derivations, triangular algebras, subspace lattice algebras, Jordan derivable maps

Abstract: Let A be a unital algebra and M be a unital A-bimodule. A linear map δ:A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ◦ B + A ◦ δ(B)=δ(A ◦ B) for any A, B ∈ A, with A ◦ B=P, here A ◦ B=AB + BA is the usual Jordan product. In this article, we show that if A=AlgN is a Hilbert space nest algebra and M=B(H), or A=M=B(X), then, a linear map δ:A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Key words: Derivations, triangular algebras, subspace lattice algebras, Jordan derivable maps

薛天娇, 安润玲, 侯晋川. CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS[J]. 数学物理学报(英文版), 2017, 37(3): 668-678.

Tianjiao XUE, Runling AN, Jinchuan HOU. CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS[J]. Acta mathematica scientia,Series B, 2017, 37(3): 668-678.

参考文献

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CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

CHARACTERIZATION OF DERIVATIONS ON B(X) BY LOCAL ACTIONS

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