Data di Pubblicazione:
2012
Citazione:
Covering the unit sphere of certain Banach spaces by sequences of slices and balls / V. P. Fonf, C. Zanco. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 0008-4395. - 57 (2014):1(2012 Sep 21), pp. 42-50. [10.4153/CMB-2012-027-7]
Abstract:
We prove that, given any covering of any infinite-dimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a point-finite covering by the union of countably many slices of the unit ball.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
point finite coverings ; slices ; polyhedral spaces ; Hilbert spaces
Elenco autori:
V.P. Fonf, C. Zanco
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