Banach Journal of Mathematical Analysis

Harmonic functionals on certain Banach algebras

Mehdi Nemati

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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

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

First available in Project Euclid: 19 December 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Generalized Fourier algebras harmonic functionals $\phi$-mean


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.

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