Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 1 (2018), 231-246.
On a class of Banach algebras associated to harmonic analysis on locally compact groups and semigroups
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.
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
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.aot/1512497960