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

Tom 227 / 2014

Mikhail I. Ostrovskii Fundamenta Mathematicae 227 (2014), 85-95 MSC: Primary 30L05; Secondary 46B22, 46B85. DOI: 10.4064/fm227-1-6

Streszczenie

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.

Autorzy

  • Mikhail I. OstrovskiiDepartment of Mathematics and Computer Science
    St. John's University
    8000 Utopia Parkway
    Queens, NY 11439, U.S.A.
    e-mail

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