Groupoids and Hermitian Banach *-algebras

2021/05/31 by Are Austad, Austad, Are, Eduard Ortega +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2105.14793

openalex publication_date 2021/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study when the twisted groupoid Banach *-algebra L¹(G,σ) is Hermitian. In particular, we prove that Hermitian groupoids satisfy the weak containment property. Furthermore, we find that for L¹(G,σ) to be Hermitian it is sufficient that L¹ (G_σ) is Hermitian. Moreover, if G is ample, we find necessary conditions for L¹(G,σ) to be Hermitian in terms of the fibers G^x_x.

Cited by

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

Related

• Hermitian crossed product Banach algebras
• Banach algebras associated to twisted étale groupoids: inverse semigroup disintegration and representations on L^p-spaces
• Banach algebras associated to twisted étale groupoids: simplicity and pure infiniteness
• Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras
• Generalised Twisted Groupoids and their C*-algebras