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Constructions of the maximal strongly character invariant segal algebras and their applications

Part of: Abstract harmonic analysis Locally compact abelian groups

Published online by Cambridge University Press:  09 April 2009

Chang-Pao Chen
Chang-Pao Chen
Affiliation:
Institute of Mathematics National Tsing Hua UniversityHsinchu, Taiwan 300 Republic of, China
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Abstract

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Let G denote any locally compact abelian group with the dual group Γ. We construct a new kind of subalgebra L1(G) ⊗ΓS of L1(G) from given Banach ideal S of L1(G). We show that L1(G) ⊗гS is the larger amoung all strongly character invariant homogeneous Banach algebras in S. when S contains a strongly character invariant Segal algebra on G, it is show that L1(G) ⊗гS is also the largest among all strongly character invariant Segal algebras in S. We give applications to characterizations of two kinds of subalgebras of L1(G)-strongly character invariant Segal algebras on G and Banach ideal in L1(G) which contain a strongly character invariant Segal algebra on G.

Keywords

Banach idealhomogeneous Banach algebraSegal algebrastrongly character invariantlocally compact abelian group.

MSC classification

Secondary: 22B10: Structure of group algebras of LCA groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 1 , August 1983 , pp. 123 - 131
Copyright
Copyright © Australian Mathematical Society 1983

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