Characterizations of all-derivable points in nest algebras

2011/07/11 by Jun Zhu, Zhu, Jun, Sha Zhao +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1107.1931

8 pages

arxiv created 2011/07/11 · arxiv updated 2011/07/12

Abstract

Let A be an operator algebra on a Hilbert space. We say that an element G∈ A is an all-derivable point of A if every derivable linear mapping ϕ at G (i.e. ϕ(ST)=ϕ(S)T+Sϕ(T) for any S,T∈ algN with ST=G) is a derivation. Suppose that N is a nontrivial complete nest on a Hilbert space H. We show in this paper that G∈ algN is an all-derivable point if and only if G≠0.

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