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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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