A well known result due to H. Corson has been recently improved by the authors. In its final form it essentially reads as follows: for any covering $\tau$ by closed bounded convex subsets of any Banach space $X$ containing a separable infinite-dimensional dual space, a (algebraically) finite-dimensional compact set $C$ can always be found that meets infinitely many members of $\tau$. In the present paper we investigate how small the dimension of this compact set can be, in the case the members of $\tau$ are closed bounded convex bodies satisfying general conditions of rotundity or smoothness type. In particular, such a compact set turns out to be a segment whenever the members of $\tau$ are rotund or smooth bodies in the usual sense.

Coverings of Banach spaces: beyond the Corson theorem / V.P. Fonf, C. Zanco. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 21:3(2009), pp. 533-546.

Coverings of Banach spaces: beyond the Corson theorem

C. Zanco
Ultimo
2009

Abstract

A well known result due to H. Corson has been recently improved by the authors. In its final form it essentially reads as follows: for any covering $\tau$ by closed bounded convex subsets of any Banach space $X$ containing a separable infinite-dimensional dual space, a (algebraically) finite-dimensional compact set $C$ can always be found that meets infinitely many members of $\tau$. In the present paper we investigate how small the dimension of this compact set can be, in the case the members of $\tau$ are closed bounded convex bodies satisfying general conditions of rotundity or smoothness type. In particular, such a compact set turns out to be a segment whenever the members of $\tau$ are rotund or smooth bodies in the usual sense.
covering ; locally finite covering ; finitely locally finite covering
Settore MAT/05 - Analisi Matematica
2009
http://hdl.handle.net/2434/38203
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/67513
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact