The geometry of Hamming-type metrics and their embeddings into Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355107" target="_blank" >RIV/68407700:21230/21:00355107 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11856-021-2187-0" target="_blank" >https://doi.org/10.1007/s11856-021-2187-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-021-2187-0" target="_blank" >10.1007/s11856-021-2187-0</a>

Result language
angličtina
Original language name
The geometry of Hamming-type metrics and their embeddings into Banach spaces
Original language description
Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic-c(0) spaces in terms of a bi-Lipschitz invariant which involves metrics that generalize the Hamming metric on k-subsets of N. We apply this characterization to show that the class of separable, reflexive, and asymptotic-c(0) Banach spaces is non-Borel co-analytic. Finally, we introduce a relaxation of the asymptotic-c(0) property, called the asymptotic-subsequential-c(0) property, which is a partial obstruction to the equi-coarse embeddability of the sequence of Hamming graphs. We present examples of spaces that are asymptotic-subsequential-c(0). In particular, T*(T*) is asymptotic-subsequential-c(0) where T* is Tsirelson's original space.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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