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Denseness of operators which attain their numerical radius

Published online by Cambridge University Press:  17 April 2009

Wang Jia-Ping  and
Yu Xin Tai
Wang Jia-Ping
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, China
Yu Xin Tai
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, China
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We show that a bounded linear operator on a dual Banach space X may be perturbed by a compact operator of arbitrarily small norm to yield an operator which attains its numerical radius provided the weak star and norm topologies coincide on the unit sphere of X.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 31 - 34
Copyright
Copyright © Australian Mathematical Society 1993

References

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