Advances in Operator Theory

On a class of Banach algebras associated to harmonic analysis on locally compact groups and semigroups

Anthony To-Ming Lau and Hung Le Pham

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The purpose of this paper is to present some old and recent results for the class of $F$-algebras which include most classes of Banach algebras that are important in abstract harmonic analysis. We also introduce a subclass of the class of $F$-algebras, called normal $F$-algebras, that captures better the measure algebras and the (reduced) Fourier-Stieltjes algebras, and use this to give new characterisations the reduced Fourier-Stieltjes algebras of discrete groups.

Article information

Adv. Oper. Theory, Volume 3, Number 1 (2018), 231-246.

Received: 11 February 2017
Accepted: 29 June 2017
First available in Project Euclid: 5 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Secondary: 46J05: General theory of commutative topological algebras 22D10: Unitary representations of locally compact groups

Fourier algebra locally compact group group algebra Fourier–Stieltjes algebra F-algebra


Lau, Anthony To-Ming; Pham, Hung Le. On a class of Banach algebras associated to harmonic analysis on locally compact groups and semigroups. Adv. Oper. Theory 3 (2018), no. 1, 231--246. doi:10.22034/aot.1702-1115.

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