Espaces de Banach stables

Krivine, Jean-Louis; Maurey, Bernard

doi:10.1007/bf02761674

Cited by 122 publications

(107 citation statements)

References 8 publications

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“…By [28,Corollary 4.5], this is true for subspaces of L p , 1 ă p ă 8 and for subspaces of L 1 not containing 1 , because any such space has property pm r q for some r ą 1. More generally, this is true for separable Banach spaces not containing 1 which are stable in the sense of [33]; see the proof of [27, Theorem 3.10].…”

Section: Almost Isometric Embeddingsmentioning

confidence: 99%

Smoothness, asymptotic smoothness and the Blum-Hanson property

2015

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Abstract. We isolate various sufficient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of asymptotic smoothness of X has an extremal behaviour at infinity, or if X is uniformly Gâteaux smooth and embeds isometrically into a Banach space with a 1-unconditional finite-dimensional decomposition.

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Section: Almost Isometric Embeddingsmentioning

confidence: 99%

Smoothness, asymptotic smoothness and the Blum-Hanson property

2015

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“…The notion of stability was introduced, originally for (separable) Banach spaces, in the work of Krivine and Maurey [20], in an attempt to exhibit a class of Banach spaces with a very regular linear structure. It seems that its natural extension to general metric spaces was rst studied by Garling [10].…”

Section: Nearly Isometric Embeddability Of Stable Metric Spacesmentioning

confidence: 99%

Tight Embeddability of Proper and Stable Metric Spaces

Baudier

Lancien

2015

Analysis and Geometry in Metric Spaces

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Abstract:We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [ , ∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the n p 's. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of re exive Banach spaces.

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“…The notion of stability inside a model appears for example in the work of Krivine and Maurey on stable Banach spaces [KM81]: a Banach space E is stable in the sense of Krivine and Maurey precisely if the formula x + y is stable in the unit ball of E (viewed as a continuous structure in an appropriate language) in the sense defined below.…”

Section: Proposition 711 ϕ Is Stable If and Only If For One (Any)mentioning

confidence: 99%