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On the
preservation of properties by piecewise affine maps of
locally compact groups
Serina Camungol, Matthew Morison, Skylar Nicol and Ross Stokke
Vol. 12 (2019), No. 3, 491–502
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Abstract |
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As shown by Cohen (1960) and Ilie and Spronk (2005), for locally compact groups and , there is a one-to-one correspondence between the completely bounded homomorphisms of their respective Fourier and Fourier–Stieltjes algebras and piecewise affine continuous maps . 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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Keywords
locally compact group, piecewise affine map, amenability,
Fourier algebra
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Mathematical Subject Classification 2010
Primary: 22D05, 43A22, 43A07, 43A30
Secondary: 20E99
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Milestones
Received: 27 February 2018
Accepted: 9 September 2018
Published: 14 December 2018
Communicated by David Royal Larson
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Authors |
| Serina Camungol | |
| Department of Mathematics and
Statistics University of Winnipeg Winnipeg, MB Canada |
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| Matthew Morison | |
| Department of Mathematics and
Statistics University of Winnipeg Winnipeg, MB Canada |
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| Skylar Nicol | |
| Department of Mathematics and
Statistics University of Winnipeg Winnipeg, MB Canada |
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| Ross Stokke | |
| Department of Mathematics and
Statistics University of Winnipeg Winnipeg, MB Canada |
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