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Infinite-Dimensional Polyhedrality |
Canad. J. Math. 56(2004), 472-494
Published:2004-06-01
Printed: Jun 2004
Printed: Jun 2004
- Vladimir P. Fonf
- Libor Veselý
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 - 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 |