Characterizations of left derivable maps at non-trivial idempotents on nest algebras

2013/12/25 by Hoger Ghahramani, Ghahramani, Hoger · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1312.6959

openalex publication_date 2013/12/25 · arxiv created 2014/01/02 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Alg N be a nest algebra associated with the nest N on a (real or complex) Banach space \X. Suppose that there exists a non-trivial idempotent P∈ AlgN with range P(\X) ∈ N and δ:AlgN → AlgN is a continuous linear mapping (generalized) left derivable at P, i.e. δ(ab)=aδ(b)+bδ(a) (δ(ab)=aδ(b)+bδ(a)-baδ(I)) for any a,b∈ AlgN with ab=P. we show that δ is a (generalized) Jordan left derivation. Moreover, we characterize the strongly operator topology continuous linear maps δ on some nest algebra AlgN with property that δ(P)=2Pδ(P) or δ(P)=2Pδ(P)-Pδ(I) every idempotent P in AlgN.

Cited by

• Left derivable or Jordan left derivable mappings on Banach algebras

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