On the invertibility of elementary operators

2013/12/04 by Nadia Boudi, Boudi, Nadia, Janko Bračič +1
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.1312.1307

arxiv created 2013/12/04 · openalex publication_date 2013/12/04 · arxiv updated 2013/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathscrX be a complex Banach space and L(\mathscrX) be the algebra of all bounded linear operators on \mathscrX. For a given elementary operator Φ of length 2 on L(\mathscrX), we determine necessary and sufficient conditions for the existence of a solution of the equation \rm X Φ=0 in the algebra of all elementary operators on L(\mathscrX). Our approach allows us to characterize some invertible elementary operators of length 2 whose inverses are elementary operators.

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