文献类型：期刊文献

英文题名：On derivable mappings

作者：Li, Jiankui[2];Pan, Zhidong[1]

机构：[1]Saginaw Valley State Univ, Dept Math, University Ctr, MI 48710 USA;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2011

卷号：374

期号：1

起止页码：311

外文期刊名：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000282707700025)】；

基金：This work was completed with the support of NSF of China and the Ruth and Ted Braun Fellowship from the Saginaw Community Foundation.

语种：英文

外文关键词：Derivation; Jordan derivation; Nest

摘要：A linear mapping delta from an algebra A into an A-bimodule M is called derivable at c is an element of A if delta(a)b a delta(b) = delta(c) for all a, b is an element of A with ab = c. For a norm-closed unital subalgebra A of operators on a Banach space X, we show that if C is an element of A has a right inverse in B(X) and the linear span of the range of rank-one operators in A is dense in X then the only derivable mappings at C from A into B(X) are derivations; in particular the result holds for all completely distributive subspace lattice algebras, J-subspace lattice algebras, and norm-closed unital standard algebras of B(X). As an application, every Jordan derivation from such an algebra into B(X) is a derivation. For a large class of reflexive algebras A on a Banach space X, we show that inner derivations from A into B(X) can be characterized by boundedness and derivability at any fixed C is an element of A. provided C has a right inverse in B(X). We also show that if A is a canonical subalgebra of an AF C*-algebra B and M is a unital Banach A-bimodule, then every bounded local derivation from A into M is a derivation; moreover, every bounded linear mapping from A into B that is derivable at the unit I is a derivation. (C) 2010 Elsevier Inc. All rights reserved.