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Stable linear maps

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

Published online by Cambridge University Press:  26 February 2010

M. C. Irwin
M. C. Irwin
Affiliation:
Department of Pure Mathematics, University of Liverpool.
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Extract

Let ˜ be an equivalence relation on a topological space X. A point x ε X i s stable with respect to ˜ if it is in the interior of an equivalence class. We may also add, if ambiguity arises, that x is stable under perturbations in X. Let E be a Banach space, and let L(E) be the Banach space of continuous linear endomorphisms of E, with norm given by |T| = sup{ |T(x) | : |x| = 1}. In this paper we discuss stability of elements of L(E) with respect to some natural equivalence relations.

MSC classification

Secondary: 47A99: None of the above, but in this section 46B99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 276 - 282
Copyright
Copyright © University College London 1971

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