Jordan and Jordan Higher All-derivable Points of Some Algebras

Jiankui Li; Zhidong Pan; Qihua Shen

Jordan and Jordan Higher All-derivable Points of Some Algebras

Operator Algebras 2012-03-13 v1

Authors: Jiankui Li , Zhidong Pan , Qihua Shen

Abstract

In this paper, we characterize Jordan derivable mappings in terms of 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 $\mathcal{N}$ on a Banach $X$ with the associated nest algebra $alg\mathcal{N}$ , if there exists a non-trivial element in $\mathcal{N}$ which is complemented in $X$ , then every $C\in alg\mathcal{N}$ is a Jordan all-derivable point of $L(alg\mathcal{N}, B(X))$ and a Jordan higher all-derivable point of $L(alg\mathcal{N})$ .

Keywords

Jordan derivable mapping Peirce decomposition Jordan all-derivable point Jordan higher derivable mapping nest algebra Banach space

Cite

@article{arxiv.1203.2481,
  title  = {Jordan and Jordan Higher All-derivable Points of Some Algebras},
  author = {Jiankui Li and Zhidong Pan and Qihua Shen},
  journal= {arXiv preprint arXiv:1203.2481},
  year   = {2012}
}

Jordan and Jordan Higher All-derivable Points of Some Algebras

Abstract

Keywords

Cite

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