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Tight Embeddability of Proper and Stable Metric Spaces

100%

Baudier F., Lancien G.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.

A new metric invariant for Banach spaces

81%

Baudier F., Kalton N., Lancien G.

Studia Mathematica

2010

tom 199

nr 1

73-94

We show that if the Szlenk index of a Banach space X is larger than the first infinite ordinal ω or if the Szlenk index of its dual is larger than ω, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into X. We show that the converse is true when X is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Studia Mathematica

2 Baudier F.

2 Lancien G.

1 Kalton N.

1 2015

1 2010

Wyniki wyszukiwania

Tight Embeddability of Proper and Stable Metric Spaces

A new metric invariant for Banach spaces