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A Note on the Topological Group c0

Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Axioms 2018, 7(4), 77; https://doi.org/10.3390/axioms7040077
Received: 28 September 2018 / Revised: 22 October 2018 / Accepted: 24 October 2018 / Published: 29 October 2018
(This article belongs to the Collection Topological Groups)
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Abstract

A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions. View Full-Text
Keywords: Gromov’s compactification; group representation; matrix coefficient; semigroup compactification; tame function Gromov’s compactification; group representation; matrix coefficient; semigroup compactification; tame function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Megrelishvili, M. A Note on the Topological Group c0. Axioms 2018, 7, 77.

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