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Normal-equivalent operators and operators with dual of scalar-type

Published online by Cambridge University Press:  20 January 2009

M. B. Ghaemi
M. B. Ghaemi
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK (mbg@maths.gla.ac.uk)
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Abstract

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If T ∈ L(X) is such that T′ is a scalar-type prespectral operator, then Re T′ and Im T′ are both dual operators. It is shown that that the possession of a functional calculus for the continuous functions on the spectrum of T is equivalent to T′ being scalar-type prespectral of class X, thus answering a question of Berkson and Gillespie.

Keywords

hermitiannormalscalar typeprespectraloperatorfunctional calculus

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 261 - 268
Copyright
Copyright © Edinburgh Mathematical Society 2000

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