Jordan and Jordan higher all-derivable points of some algebras

• Published in: Linear & multilinear algebra Vol. 61; no. 6; pp. 831 - 845
• Main Authors: Li, Jiankui, Pan, Zhidong, Shen, Qihua
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01-06-2013; Taylor & Francis Ltd
• Subjects: Algebra; Banach space; Decomposition; Jordan all-derivable point; Jordan derivation; Jordan higher all-derivable point; Jordan higher derivation; Mapping; nest algebra; Primary: 47L35; Secondary: 16W25
• ISSN: 0308-1087; 1563-5139
• DOI: 10.1080/03081087.2012.709245

In this article, we characterize Jordan derivable mappings in terms of the Peirce decomposition and determine Jordan all-derivable points for some general bimodules. Then we generalize the results to the case of Jordan higher derivable mappings. An immediate application of our main results shows that for a nest on a Banach space X with the associated nest algebra alg  , if there exists a non-trivial element in that is complemented in X, then every C ∈ alg  is a Jordan all-derivable point of L(alg  , B(X)) and a Jordan higher all-derivable point of L(alg  ).