The isomorphic Kottman constant of a Banach space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00531287" target="_blank" >RIV/67985840:_____/20:00531287 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/15079" target="_blank" >https://doi.org/10.1090/proc/15079</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/15079" target="_blank" >10.1090/proc/15079</a>
Alternative languages
Result language
angličtina
Original language name
The isomorphic Kottman constant of a Banach space
Original language description
We show that the Kottman constant $ K(cdot )$, together with its symmetric and finite variations, is continuous with respect to the Kadets metric, and they are log-convex, hence continuous, with respect to the interpolation parameter in a complex interpolation schema. Moreover, we show that $ K(X)cdot K(X^*)geqslant 2$ for every infinite-dimensional Banach space $ X$. nWe also consider the isomorphic Kottman constant (defined as the infimum of the Kottman constants taken over all renormings of the space) and solve the main problem left open in [Banach J. Math. Anal. 11 (2017), pp. 348-362], namely that the isomorphic Kottman constant of a twisted-sum space is the maximum of the constants of the respective summands. Consequently, the Kalton-Peck space may be renormed to have the Kottman constant arbitrarily close to $ sqrt {2}$. For other classical parameters, such as the Whitley and the James constants, we prove the continuity with respect to the Kadets metric. n
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
<a href="/en/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Linear-analysis techniques in operator algebras and vice versa</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
148
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
4361-4375
UT code for WoS article
000562957700021
EID of the result in the Scopus database
2-s2.0-85096345465