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Self-induced compactness in Banach spaces


Casazza, P G; Jarchow, H (1996). Self-induced compactness in Banach spaces. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 126(02):355-362.

Abstract

We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation property

Abstract

We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation property

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Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Language:English
Date:1 January 1996
Deposited On:11 Oct 2018 14:47
Last Modified:24 Nov 2018 03:03
Publisher:Cambridge University Press
ISSN:0308-2105
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1017/s0308210500022770
Related URLs:https://www.swissbib.ch/Search/Results?lookfor=nationallicencecambridge101017S0308210500022770 (Library Catalogue)

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