## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 January 2019

https://projecteuclid.org/euclid.bbms/1547780429

Digital Object Identifier
doi:10.36045/bbms/1547780429

Mathematical Reviews number (MathSciNet)
MR3901840

Zentralblatt MATH identifier
07038546

#### Citation

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