Notes on amenability

2010/12/07 by Miad Makareh Shireh, Shireh, Miad Makareh
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1012.1389

openalex publication_date 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a Banach algebra A with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^opand the amenability of A are equivalent. Also if A is a closed ideal in a commutative Banach algebra B, then the weak amenability of the projective tensor product of A and B implies the weak amenability of A.

Related

• Approximate amenability of tensor products of Banach algebras
• Relative amenability of Banach algebras
• Cohomological properties of different types of weak amenability
• Δ-weak character amenability of certain Banach algebras
• Perturbations of Banach algebras and amenability