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Gaps between Spheres in Normed Linear Spaces

Published online by Cambridge University Press:  20 November 2018

Robert H. Lohman
Robert H. Lohman*
Affiliation:
Department of Mathematics Kent State University Kent, Ohio 44242
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Abstract

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The geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.

Keywords

46B99Gapgap pointreflexivefinite-dimensionalweakly compactly generatedweak*-basic sequence

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980, pp. 347 - 354
Copyright
Copyright © Canadian Mathematical Society 1980

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