Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics

• Autorzy: Mikhail I. Ostrovskii
• Języki publikacji: EN

Abstrakty

EN

We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz image of a thick family of geodesics.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B85: Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science
• 30L05: Geometric embeddings of metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 227
• Numer: 1
• Strony: 85-95

Daty

wydano

2014

Twórcy

autor

Mikhail I. Ostrovskii

• Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, U.S.A.

Identyfikatory

DOI

10.4064/fm227-1-6