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december 2018 Invariant $\varphi$-means for abstract Segal algebras related to locally compact groups
Hossein Javanshiri, Mehdi Nemati
Bull. Belg. Math. Soc. Simon Stevin 25(5): 687-698 (december 2018). DOI: 10.36045/bbms/1547780429

Abstract

In this paper, for a locally compact group ${\mathcal G}$ we characterize character amenability and character contractibility of abstract Segal algebras with respect to the group algebra $L^1({\mathcal G})$ and the generalized Fourier algebra $A_p({\mathcal G})$. As a main result we prove that ${\mathcal G}$ is discrete and amenable if and only if some class of abstract Segal algebras in $L^1({\mathcal G})$ is character amenable. We also prove a similar result for abstract Segal algebras in $A_p({\mathcal G})$ and $C_0({\mathcal G})$. Finally, under some conditions we investigate when a commutative, semisimple, Tauberian Banach algebra is an ideal in its second dual space.

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Hossein Javanshiri. Mehdi Nemati. "Invariant $\varphi$-means for abstract Segal algebras related to locally compact groups." Bull. Belg. Math. Soc. Simon Stevin 25 (5) 687 - 698, december 2018. https://doi.org/10.36045/bbms/1547780429

Information

Published: december 2018
First available in Project Euclid: 18 January 2019

zbMATH: 07038546
MathSciNet: MR3901840
Digital Object Identifier: 10.36045/bbms/1547780429

Subjects:
Primary: ‎43A07‎, 46H05
Secondary: 46H25

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 5 • december 2018
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