Jordan and Jordan higher all-derivable points of some algebras

摘要

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 N on a Banach space X with the associated nest algebra alg N, if there exists a non-trivial element in N that is complemented in X, then every C ∈ alg N is a Jordan all-derivable point of L(alg N, B(X)) and a Jordan higher all-derivable point of L(alg N).