Jordan and Jordan Higher All-derivable Points of Some Algebras

Details Jordan and Jordan Higher All-derivable Points of Some Algebras Jordan and Jordan Higher All-derivable Points of Some Algebras

2012-03-12

arxiv.org/abs/1203.2481v1

Mathematics

Operator Algebras

Scientific paper

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 $L(alg\mathcal{N})$.

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