Symmetrized pseudofunction algebras from L^p-representations and amenability of locally compact groups

2024/11/12 by Emilie Elkiær, Elkiær, Emilie Mai · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2411.07710

openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show via an application of techniques from complex interpolation theory how the L^p-pseudofunction algebras of a locally compact group G can be understood as sitting between L¹(G) and C^*(G). Motivated by this, we collect and review various characterizations of group amenability connected to the p-pseudofunction algebra of Herz and generalize these to the symmetrized setting. Along the way, we describe the Banach space dual of the symmetrized pseudofuntion algebras on G associated with representations on reflexive Banach spaces.

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• Rigidity of pseudofunction algebras of ample groupoids
• On the continuity of derivations over locally regular Banach algebras

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