Left derivable or Jordan left derivable mappings on Banach algebras

2015/07/05 by Yana Ding, Ding, Yana, Jiankui Li +1
Mathematics · #47B47 #47B49 #47L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:47B47 #msc:47B49 #msc:47L10

paper · pdf · doi:10.48550/arxiv.1507.01301

18 pages, 0 figure

arxiv created 2015/07/05 · openalex publication_date 2015/07/05 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d be a linear mapping from a unital Banach algebra A into a unital left A-module M, and w in Z(A) be a left separating point of M. We show that the following three conditions are equivalent: (i) d is a Jordan left derivation; (ii) d is left derivable at w; (iii) d is Jordan left derivable at w. Let A be a Banach algebra with the property (B), and M be a Banach left A-module. We consider the relations between generalized (Jordan) left derivations and (Jordan) left derivable mappings at zero from A into M.

Citations

• Characterizations of left derivable maps at non-trivial idempotents on nest algebras
• Continuous linear maps on reflexive algebras behaving like Jordan left derivations at idempotent-product elements

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