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Self-induced compactness in Banach spaces

Published online by Cambridge University Press:  14 November 2011

P. G. Casazza  and
H. Jarchow
P. G. Casazza
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Mo 65211, U.S.A. e-mail: Pete@casazza.cs.missouri.edu
H. Jarchow
Affiliation:
Mathematisches Institut, Universität Zürich, CH 8057 Zürich, Switzerland e-mail: jarchow@math.unizh.ch
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Extract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 355 - 362
Copyright
Copyright © Royal Society of Edinburgh 1996

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