A NEW COARSELY RIGID CLASS OF BANACH SPACES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355109" target="_blank" >RIV/68407700:21230/21:00355109 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/S1474748019000732" target="_blank" >https://doi.org/10.1017/S1474748019000732</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1474748019000732" target="_blank" >10.1017/S1474748019000732</a>

Result language
angličtina
Original language name
A NEW COARSELY RIGID CLASS OF BANACH SPACES
Original language description
We prove that the class of reflexive asymptotic-c(0) Banach spaces is coarsely rigid, meaning that if a Banach space X coarsely embeds into a reflexive asymptotic-c(0) space Y, then X is also reflexive and asymptotic-c(0). In order to achieve this result, we provide a purely metric characterization of this class of Banach spaces. This metric characterization takes the form of a concentration inequality for Lipschitz maps on the Hamming graphs, which is rigid under coarse embeddings. Using an example of a quasi-reflexive asymptotic-c(0) space, we show that this concentration inequality is not equivalent to the non-equi-coarse embeddability of the Hamming graphs.
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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