A note on the topological group c0

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Abstract

A well-known result of Ferri and Galindo asserts that the topological group c0 is not reflexively representable and the algebra WAP(c0) 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(c0) of tame functions. Respectively, it is an open question if c0 is representable on a Rosenthal Banach space. In the present work we show that Tame(c0) is small in a sense that the unit sphere S and 2S cannot be separated by a tame function f ∈ Tame(c0). As an application we show that the Gromov's compactification of c0 is not a semigroup compactification. We discuss some questions.

Original languageEnglish
Article number77
JournalAxioms
Volume7
Issue number4
DOIs
StatePublished - 29 Oct 2018

Bibliographical note

Publisher Copyright:
© 2018 by the authors.

Keywords

  • Gromov's compactification
  • Group representation
  • Matrix coefficient
  • Semigroup compactification
  • Tame function

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