Characterizing derivations for any nest algebras on Banach spaces by their behaviors at an injective operator

2013/11/21 by Yanfang Zhang, Zhang, Yanfang, Jinchuan Hou +3
Mathematics · #47B47 #47L35 #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:47L35

paper · pdf · doi:10.48550/arxiv.1311.5276

20 pages

arxiv created 2013/11/21 · openalex publication_date 2013/11/21 · arxiv updated 2013/11/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let \mathcal N be a nest on a complex Banach space X and let Alg\mathcal N be the associated nest algebra. We say that an operator Z∈ Alg\mathcal N is an all-derivable point of Alg\mathcal N if every linear map δ from Alg\mathcal N into itself derivable at Z (i.e. δ satisfies δ(A)B+Aδ(B)=δ(Z) for any A,B ∈ Alg\mathcal N with AB=Z) is a derivation. In this paper, it is shown that every injective operator and every operator with dense range in Alg\mathcal N are all-derivable points of Alg\mathcal N without any additional assumption on the nest.

Related

• Characterizations of all-derivable points in nest algebras
• Characterizations of left derivable maps at non-trivial idempotents on nest algebras
• Lie-Type Derivations of Nest Algebras on Banach Spaces
• Jordan Higher All-Derivable Points in Nest Algebras
• Characterization of (α,α)-derivation on B(X)