Bulletin of the Belgian Mathematical Society - Simon Stevin

Invariant $\varphi$-means for abstract Segal algebras related to locally compact groups

Hossein Javanshiri and Mehdi Nemati

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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.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 5 (2018), 687-698.

First available in Project Euclid: 18 January 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A07: Means on groups, semigroups, etc.; amenable groups 46H05: General theory of topological algebras
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Banach algebra $\varphi$-amenability $\varphi$-contractibility locally compact group abstract Segal algebra


Javanshiri, Hossein; Nemati, Mehdi. Invariant $\varphi$-means for abstract Segal algebras related to locally compact groups. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 687--698. doi:10.36045/bbms/1547780429. https://projecteuclid.org/euclid.bbms/1547780429

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