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Infinite-Dimensional Polyhedrality

Published online by Cambridge University Press:  20 November 2018

Vladimir P. Fonf  and
Libor Veselý
Vladimir P. Fonf
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel e-mail: fonf@math.bgu.ac.il
Libor Veselý
Affiliation:
Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50, 20133 Milano, Italy e-mail: vesely@mat.unimi.it
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Abstract

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This paper deals with generalizations of the notion of a polytope to infinite dimensions. The most general definition is the following: a bounded closed convex subset of a Banach space is called a polytope if each of its finite-dimensional affine sections is a (standard) polytope.

We study the relationships between eight known definitions of infinite-dimensional polyhedrality. We provide a complete isometric classification of them, which gives solutions to several open problems. An almost complete isomorphic classification is given as well (only one implication remains open).

Keywords

46B2046B0346B0452B99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 3 , 01 June 2004 , pp. 472 - 494
Copyright
Copyright © Canadian Mathematical Society 2004

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