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Uniform Mazur's Intersection Property of Balls

Published online by Cambridge University Press:  20 November 2018

J. H. M. Whitfield  and
V. Zizler
J. H. M. Whitfield
Affiliation:
Department of Mathematical Sciences Lakehead University Thunder Bay, Ontario P7B 5E1 Canada
V. Zizler
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1 Canada
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Abstract

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We give a dual characterization of the following uniformization of the Mazur's intersection property of balls in a Banach space X: for every ∊ > 0 there is a K > 0 such that whenever a closed convex set C ⊂ X and a point p ∊ X are such that diam C ≤ 1/∊ and dist(p, C) ≤ ∊, then there is a closed ball B of radius ≤ K with B ⊃ C and dist(p,B) ≥ ∊/2.

Keywords

46B20ball intersection propertysmoothness
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 455 - 460
Copyright
Copyright © Canadian Mathematical Society 1987

References

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