Jordan Higher All-Derivable Points in Nest Algebras

2011/12/23 by Nannan Zhen, Jun Zhu, Zhen, Nannan +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1112.5590

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arxiv created 2011/12/23 · arxiv updated 2011/12/26

Abstract

Let N be a non-trivial and complete nest on a Hilbert space H. Suppose d=\d_n: n∈ N\ is a group of linear mappings from AlgN into itself. We say that d=\d_n: n∈ N\ is a Jordan higher derivable mapping at a given point G if d_n(ST+ST)=∑_i+j=n\d_i(S)d_j(T)+d_j(T)d_i(S)\ for any S,T∈ Alg N with ST=G. An element G∈ Alg N is called a Jordan higher all-derivable point if every Jordan higher derivable mapping at G is a higher derivation. In this paper, we mainly prove that any given point G of AlgN is a Jordan higher all-derivable point. This extends some results in \citeChen11 to the case of higher derivations.

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