Simplicity of L^p-graph algebras

2023/07/09 by Guillermo Cortiñas⋆, Cortiñas, Guillermo, Diego Montero +3
Mathematics · #16G20 #46L55 #47L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2307.05555

openalex publication_date 2023/07/09 · openalex created_date 2023/07/14 · openalex updated_date 2026/07/28

Abstract

For each 1≤ p<∞ and each countable directed graph E we consider the Leavitt path ℂ-algebra L(E) and the L^p-operator graph algebra O^p(E). We show that the (purely infinite) simplicity of O^p(E) as a Banach algebra is equivalent to the (purely infinite) simplicity of L(E) as a ring.

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