Banach Journal of Mathematical Analysis

Harmonic functionals on certain Banach algebras

Mehdi Nemati

Abstract

In this paper, we study the concept of harmonic functionals for certain Banach algebras such as generalized Fourier algebras. For a non-zero character $\phi$ on Banach algebra ${\mathcal A}$, we also characterize the concept of $\phi$-amenability in terms of harmonic functionals. Finally, for a locally compact group $G$ we investigate the space $H_{\sigma, x}$ of $\sigma$-harmonic functionals in the dual of generalized Fourier algebra $A_p(G)$. The main result states that $G$ is first countable if and only if $\sigma$ is adapted if and only if $H_{\sigma, x}={\Bbb C}\phi_x$.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 1 (2015), 159-165.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.bjma/1419000585

Digital Object Identifier
doi:10.15352/bjma/09-1-13

Mathematical Reviews number (MathSciNet)
MR3296093

Zentralblatt MATH identifier
1311.43003

Citation

Nemati , Mehdi. Harmonic functionals on certain Banach algebras. Banach J. Math. Anal. 9 (2015), no. 1, 159--165. doi:10.15352/bjma/09-1-13. https://projecteuclid.org/euclid.bjma/1419000585