Banach Journal of Mathematical Analysis

Harmonic functionals on certain Banach algebras

Mehdi Nemati

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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

Permanent link to this document
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

Subjects
Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]

Keywords
Generalized Fourier algebras harmonic functionals $\phi$-mean

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


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