Segal Frechet algebras

2015/07/23 by F. Abtahi, Abtahi, F., S. Rahnama +3
Mathematics · #46A03 #46A04 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A03 #msc:46A04

paper · pdf · doi:10.48550/arxiv.1507.06577

11 pages, 0 figures,

arxiv created 2015/07/23 · arxiv updated 2015/07/24

Abstract

Let (A,p_l)_{l∈\Bbb N} be a Frechet algebra. In this paper, we introduce the concept of Segal Frechet algebra and investigate known results about abstract Segal algebras, for Segal Frechet algebras. Also we recall the concept of approximate identities for topological algebras and provide some remarkable results for Segal Frechet algebras. Moreover, we verify ideal theorem for Frechet algebras and characterize closed ideals of Segal Frechet algebra (B,q_m)_{m∈\Bbb N} in (A,p_l)_{l∈\Bbb N}.

Related

• Frechet algebras in abstract Harmonic analysis
• n-ideal and n-weak amenability of Frechet algebras
• BSE-property for some certain Segal and Banach algebras
• Locally bounded approximate diagonal modulo an ideal of Frechet algebras
• Bochner-Schoenberg-Eberlein-type inequality of the direct sum, ideals and quotient of Frechet algebras