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On the continuous linear image of a Banach space

Part of: Normed linear spaces and Banach spaces; Banach lattices General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

R. W. Cross
R. W. Cross
Affiliation:
University of Cape TownRondebosch, South Africa
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Abstract

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A subspace of a Banach space is called an operator range if it is the continuous linear image of a Banach space. Operator ranges and operator ideals with fixed range space are investigated. Properties of strictly singular, strictly cosingular, weakly sequentially precompact, and other classes of operators are derived. Perturbation theory and closed semi-Fredholm operators are discussed in the final section.

MSC classification

Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A53: (Semi-) Fredholm operators; index theories 47A55: Perturbation theory 46B25: Classical Banach spaces in the general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 2 , March 1980 , pp. 219 - 234
Copyright
Copyright © Australian Mathematical Society 1980

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