Embedding a topological group into its WAP-compactification

Ferri, Stefano; Galindo, Juana

doi:10.4064/sm193-2-1

Cited by 6 publications

(2 citation statements)

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“…Recall that c 0 , as an additive abelian topological group, is not representable on a reflexive Banach space by a well-known result of Ferri and Galindo [8]. In fact, WAP(c 0 ) separates the points but not points and closed subsets.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Topological Group c0

Megrelishvili

2018

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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.

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Section: Introductionmentioning

confidence: 99%

A Note on the Topological Group c0

Megrelishvili

2018

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“…We refer the reader to the following related recent works: Gao and Pestov [10], Megrelishvili [20], Ferri and Galindo [8], and Galindo [9].…”

Section: Introductionmentioning

confidence: 99%

On Hilbert dynamical systems

Glasner¹,

Weiss²

2011

Ergod. Th. Dynam. Sys.

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To the memory of our dear friend, Dan Rudolph, from whom we learned so much Abstract. Returning to a classical question in harmonic analysis, we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the dual groupẐ = T, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.

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Reflexive representability and stable metrics

2009

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Abstract. It is well-known that a topological group can be represented as a group of isometries of a reflexive Banach space if and only if its topology is induced by weakly almost periodic functions (see [Sht94], [Meg01b] and [Meg07]). We show that for a metrisable group this is equivalent to the property that its metric is uniformly equivalent to a stable metric in the sense of Krivine and Maurey (see [KM81]). This result is used to give a partial negative answer to a problem of Megrelishvili.

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Embedding a topological group into its WAP-compactification

Cited by 6 publications

References 22 publications

A Note on the Topological Group c0

A Note on the Topological Group c0

On Hilbert dynamical systems

Reflexive representability and stable metrics

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