A representation of stable Banach spaces

Chaatit, Fouad

doi:10.1007/bf01196167

Cited by 4 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chaatit [Cha96] proved that the additive group of any stable separable Banach space can be represented as a group of isometries of a separable reflexive Banach space. First we show, applying results by Shtern (Fact 1.3), that any stable group is reflexively representable.…”

Section: 1mentioning

confidence: 99%

See 1 more Smart Citation

Reflexive representability and stable metrics

2009

View full text Add to dashboard Cite

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.

show abstract

Section: 1mentioning

confidence: 99%

“…Chaatit [Cha96] Proof. As in the previous result, by Lemma 3.1 we may assume that d is bounded, and using the results proved in the previous section it suffices to produce a left-invariant stable locally continuous pre-metric uniformly equivalent to d.…”

Section: 1mentioning

confidence: 99%

Reflexive representability and stable metrics

2009

View full text Add to dashboard Cite

show abstract

“…This was first proved by Chaatit [4] without referring explicitly to weakly almost periodic functions. Among stable spaces we find all L p (µ)-spaces for 1 ≤ p < ∞.…”

mentioning

confidence: 94%

Embedding a topological group into its WAP-compactification

Ferri

Galindo

2009

Studia Math.

View full text Add to dashboard Cite

Abstract. We prove that the topology of the additive group of the Banach space c0 is not induced by weakly almost periodic functions or, what is the same, that this group cannot be represented as a group of isometries of a reflexive Banach space. We show, in contrast, that additive groups of Schwartz locally convex spaces are always representable as groups of isometries on some reflexive Banach space.

show abstract

Topological transformation groups

Megrelishvili¹

2007

Open Problems in Topology II

View full text Add to dashboard Cite

A representation of stable Banach spaces

Abstract: We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.

Cited by 4 publications

References 5 publications

Reflexive representability and stable metrics

Reflexive representability and stable metrics

Embedding a topological group into its WAP-compactification

Topological transformation groups

Contact Info

Product

Resources

About