Rocky Mountain Journal of Mathematics

Cyclicity of the left regular representation of a locally compact group

Zsolt Tanko

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We combine harmonic analysis and operator algebraic techniques to give a concise argument that the left regular representation of a locally compact group is cyclic if and only if the group is first countable, a result first proved by Greenleaf and Moskowitz.

Article information

Rocky Mountain J. Math., Volume 48, Number 3 (2018), 1015-1018.

First available in Project Euclid: 2 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22D10: Unitary representations of locally compact groups
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]

Left regular representation group von Neumann algebra Fourier algebra


Tanko, Zsolt. Cyclicity of the left regular representation of a locally compact group. Rocky Mountain J. Math. 48 (2018), no. 3, 1015--1018. doi:10.1216/RMJ-2018-48-3-1015.

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