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Symmetrically separated sequences in the unit sphere of a Banach space
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SYSNO ASEP 0494452 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Symmetrically separated sequences in the unit sphere of a Banach space Author(s) Hájek, Petr Pavel (MU-W) RID, SAI
Kania, Tomasz (MU-W) SAI, ORCID, RID
Russo, T. (IT)Source Title Journal of Functional Analysis. - : Elsevier - ISSN 0022-1236
Roč. 275, č. 11 (2018), s. 3148-3168Number of pages 21 s. Language eng - English Country US - United States Keywords symmetrically separated unit vectors ; Elton–Odell theorem ; Kottman theorem ; symmetric Kottman constant Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA16-07378S GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000447961100006 EID SCOPUS 85040747352 DOI https://doi.org/10.1016/j.jfa.2018.01.008 Annotation We prove the symmetric version of Kottman's theorem, that is to say, we demonstrate that the unit sphere of an infinite-dimensional Banach space contains an infinite subset A with the property that ... for distinct elements x,y \in A, thereby answering a question of J.M.F. Castillo. In the case where X contains an infinite-dimensional separable dual space or an unconditional basic sequence, the set A may be chosen in a way that ... for some \epsilon>0 and distinct x,y \in A. Under additional structural properties of X, such as non-trivial cotype, we obtain quantitative estimates for the said \epsilon. Certain renorming results are also presented. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
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