Data di Pubblicazione:
2020
Citazione:
Star-finite coverings of Banach spaces / C.A. De Bernardi, J. Somaglia, L. Vesely. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 491:2(2020).
Abstract:
We study star-finite coverings of infinite-dimensional normed spaces. A family of sets
is called star-finite if each of its members intersects only finitely many other members
of the family. It follows from our results that an LUR or a uniformly Fréchet smooth
infinite-dimensional Banach space does not admit star-finite coverings by closed
balls. On the other hand, we present a quite involved construction of a star-finite
covering of c_0(Γ) by Fréchet smooth centrally symmetric bounded convex bodies.
A similar but simpler construction shows that every normed space of countable
dimension (and hence incomplete) has a star-finite covering by closed balls.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Covering of normed space; Frechet smooth body; Locally uniformly rotund norm;
Elenco autori:
C.A. De Bernardi, J. Somaglia, L. Vesely
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