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THE COARSE GEOMETRY OF TSIRELSON'S SPACE AND APPLICATIONS

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00323439" target="_blank" >RIV/68407700:21230/18:00323439 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1090/jams/899" target="_blank" >http://dx.doi.org/10.1090/jams/899</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1090/jams/899" target="_blank" >10.1090/jams/899</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    THE COARSE GEOMETRY OF TSIRELSON'S SPACE AND APPLICATIONS

  • Original language description

    Abstract: The main result of this article is a rigidity result pertaining to the spreading model structure for Banach spaces coarsely embeddable into Tsirelson's original space $ T^*$. Every Banach space that is coarsely embeddable into $ T^*$ must be reflexive, and all of its spreading models must be isomorphic to $ c_0$. Several important consequences follow from our rigidity result. We obtain a coarse version of an influential theorem of Tsirelson: $ T^*$ coarsely contains neither $ c_0$ nor $ ell _p$ for $ pin [1,infty )$. We show that there is no infinite-dimensional Banach space that coarsely embeds into every infinite-dimensional Banach space. In particular, we disprove the conjecture that the separable infinite-dimensional Hilbert space coarsely embeds into every infinite-dimensional Banach space. The rigidity result follows from a new concentration inequality for Lipschitz maps on the infinite Hamming graphs that take values into $ T^*$, and from the embeddability of the infinite Hamming graphs into Banach spaces that admit spreading models not isomorphic to $ c_0$. Also, a purely metric characterization of finite dimensionality is obtained.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

  • ISSN

    0894-0347

  • e-ISSN

    1088-6834

  • Volume of the periodical

    31

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    19

  • Pages from-to

    699-717

  • UT code for WoS article

    000430377800004

  • EID of the result in the Scopus database

    2-s2.0-85045897954