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2019 On the preservation of properties by piecewise affine maps of locally compact groups
Serina Camungol, Matthew Morison, Skylar Nicol, Ross Stokke
Involve 12(3): 491-502 (2019). DOI: 10.2140/involve.2019.12.491

Abstract

As shown by Cohen (1960) and Ilie and Spronk (2005), for locally compact groups G and H , there is a one-to-one correspondence between the completely bounded homomorphisms of their respective Fourier and Fourier–Stieltjes algebras φ : A ( G ) B ( H ) and piecewise affine continuous maps α : Y H G . Using elementary arguments, we show that several (locally compact) group-theoretic properties, including amenability, are preserved by certain continuous piecewise affine maps. We discuss these results in relation to Fourier algebra homomorphisms.

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Serina Camungol. Matthew Morison. Skylar Nicol. Ross Stokke. "On the preservation of properties by piecewise affine maps of locally compact groups." Involve 12 (3) 491 - 502, 2019. https://doi.org/10.2140/involve.2019.12.491

Information

Received: 27 February 2018; Accepted: 9 September 2018; Published: 2019
First available in Project Euclid: 5 February 2019

zbMATH: 07033144
MathSciNet: MR3905343
Digital Object Identifier: 10.2140/involve.2019.12.491

Subjects:
Secondary: 20E99

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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