Symmetrically separated sequences in the unit sphere of a Banach space

0494452 - MÚ 2019 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA16-07378S
Institucionální podpora: RVO:67985840
Klíčová slova: symmetrically separated unit vectors * Elton–Odell theorem * Kottman theorem * symmetric Kottman constant
Obor OECD: Pure mathematics
Impakt faktor: 1.637, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0287636