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Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls

Published online by Cambridge University Press:  20 November 2018

Vladimir P. Fonf  and
Clemente Zanco
Vladimir P. Fonf
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel e-mail: fonf@math.bgu.ac.il
Clemente Zanco
Affiliation:
Dipartimento di Matematica, Università degli Studi, Via C. Saldini, 50, 20133 Milano MI, Italy e-mail: clemente.zanco@unimi.it
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Abstract

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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.

Keywords

46B2046C0552C17point finite coveringsslicespolyhedral spacesHilbert spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 42 - 50
Copyright
Copyright © Canadian Mathematical Society 2014

References

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