Frechet algebras in abstract Harmonic analysis

2018/11/27 by Zahra Alimohammadi, Alimohammadi, Zahra, Ali Rejali +1
Mathematics · #43A20 #46H05 #46H25 #46J05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:43A20 #msc:46H05 #msc:46H25 #msc:46J05

paper · pdf · doi:10.48550/arxiv.1811.10987

arxiv created 2018/11/27 · openalex publication_date 2018/11/27 · arxiv updated 2018/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a survey of the similarities and differences between Banach and Frechet algebras including some known results and examples. We also collect some important generalizations in abstract harmonic analysis; for example, the generalization of the concepts of vector-valued Lipschitz algebras, abstract Segal algebras, Arens regularity, amenability, weak amenability, ideal amenability, etc.

Related

• An amenable, radical Banach algebra
• Segal Frechet algebras
• The BSE property for vector-valued Frechet Lipschitz algebras
• n-ideal and n-weak amenability of Frechet algebras
• On affirmative solution to Michael's acclaimed problem in the theory of Fréchet algebras, with applications to automatic continuity theory