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Denseness of operators which attain their numerical radius

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

I. D. Berg  and
Brailey Sims
I. D. Berg
Affiliation:
Department of Mathematics University of Illinois at Urbana-Champaign273 Altgeld Hall, 1409 West Green Street Urbana, Illinois 61801, U.S.A.
Brailey Sims
Affiliation:
Department of Mathematics University of New EnglandArmidale, N.S.W. 2351, Australia
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Abstract

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We show that a bounded linear operator on a uniformly convex space may be perturbed by a compact operator of arbitrarily small norm to yield an operator which attains its numerical radius.

MSC classification

Secondary: 47A12: Numerical range, numerical radius
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 130 - 133
Copyright
Copyright © Australian Mathematical Society 1984

References

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Joram, Lindenstrauss, ‘On operators which attain their norm’, Israel J. Math. 1 (1963), 139–148.Google Scholar
Brailey, Sims, On numerical range and its application to Banach algebra (Ph. D. dissertation, Universtiy of Newcastle, Australia, 1972).Google Scholar