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Self-induced compactness in Banach spaces
Published online by Cambridge University Press: 14 November 2011
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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