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Infinite-Dimensional Polyhedrality

  Published:2004-06-01
 Printed: Jun 2004
  • Vladimir P. Fonf
  • Libor Veselý
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Abstract

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 \emph{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).
MSC Classifications: 46B20, 46B03, 46B04, 52B99 show english descriptions Geometry and structure of normed linear spaces
Isomorphic theory (including renorming) of Banach spaces
Isometric theory of Banach spaces
None of the above, but in this section
46B20 - Geometry and structure of normed linear spaces
46B03 - Isomorphic theory (including renorming) of Banach spaces
46B04 - Isometric theory of Banach spaces
52B99 - None of the above, but in this section
 

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