Covering a Banach space
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- by Vladimir P. Fonf and Clemente Zanco PDF
- Proc. Amer. Math. Soc. 134 (2006), 2607-2611 Request permission
Abstract:
A well-known theorem by H. Corson states that if a Banach space admits a locally finite covering by bounded closed convex subsets, then it contains no infinite-dimensional reflexive subspace. We strengthen this result proving that if an infinite-dimensional Banach space admits a locally finite covering by bounded $w$-closed subsets, then it is $c_0$-saturated, thus answering a question posed by V. Klee concerning locally finite coverings of $l_1$ spaces. Moreover, we provide information about massiveness of the set of singular points in (PC) spaces.References
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Additional Information
- Vladimir P. Fonf
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel
- MR Author ID: 190586
- Email: fonf@math.bgu.ac.il
- Clemente Zanco
- Affiliation: Dipartimento di Matematica, Università degli Studi, via C. Saldini 50, 20133 Milano MI, Italy
- MR Author ID: 186465
- Email: zanco@mat.unimi.it
- Received by editor(s): October 20, 2004
- Received by editor(s) in revised form: March 22, 2005
- Published electronically: February 17, 2006
- Additional Notes: The first author was supported in part by Israel Science Foundation, Grant #139/03.
The second author was supported in part by the Ministero dell’Università e della Ricerca Scientifica e Tecnologica of Italy - Communicated by: N. Tomczak-Jaegermann
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2607-2611
- MSC (2000): Primary 46B20; Secondary 54E52
- DOI: https://doi.org/10.1090/S0002-9939-06-08254-2
- MathSciNet review: 2213739