A form of infinite-dimensional polytopes
type: Item
instance of: scholarly article
title: A form of infinite-dimensional polytopes
zbMATH Open document ID: 0562.46011
DOI: 10.1007/BF01077837
publication date: 1984-01-01T00:00:00Z
review text: Following Kadec, an infinite-dimensional polytope, or K-polytope is defined as a closed convex bounded subset of a Banach space such that its intersection with any finite-dimensional manifold is a polytope. Theorem. Let X be a Banach space such that its closed unit ball \(B_ X\) is a K-polytope. Let \(T:X\to Y\) be a continuous linear injective mapping into a Banach space Y with \(T(B_ X)\) closed. Then T is an isomorphism. As a consequence it is shown that the algebraic interior of a K-polytope coincides with its topological interior. Related references are [\textit{V. P. Fonf}, Mat. Zametki 30, 627-634 (1981; Zbl 0484.46019)] and [\textit{J. Lindenstrauss}, Isr. J. Math. 4 (1966), 235-242 (1967; Zbl 0148.113)].
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 3895657
zbMATH Keywords: polyhedral Banach space
zbMATH Keywords: infinite-dimensional polytope
zbMATH Keywords: K-polytope
zbMATH Keywords: algebraic interior of a K-polytope coincides with its topological interior
author: V. P. Fonf
reviewed by: Marián Fabian
MaRDI profile type: Publication
cites work: Базисные последовательности, биортогональные системы и нормирующие множества в пространствах Банаха и Фреше
cites work: Notes on Klee's paper 'Polyhedral sections of convex bodies'
cites work: Q3278543
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3895657