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Symmetrically separated sequences in the unit sphere of a Banach space
- 1.0494452 - MÚ 2019 RIV US eng J - Journal Article
Hájek, Petr Pavel - Kania, Tomasz - Russo, T.
Symmetrically separated sequences in the unit sphere of a Banach space.
Journal of Functional Analysis. Roč. 275, č. 11 (2018), s. 3148-3168. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA ČR GA16-07378S
Institutional support: RVO:67985840
Keywords : symmetrically separated unit vectors * Elton–Odell theorem * Kottman theorem * symmetric Kottman constant
OECD category: Pure mathematics
Impact factor: 1.637, year: 2018
https://www.sciencedirect.com/science/article/pii/S0022123618300223?via%3Dihub
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.
Permanent Link: http://hdl.handle.net/11104/0287636
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