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Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators

Published online by Cambridge University Press:  14 November 2011

S. Okada  and
W. Ricker
S. Okada
Affiliation:
Department of Mathematics, San Diego State University, San Diego, CA 92182-0314, U.S.A.
W. Ricker
Affiliation:
Department of Mathematics, I.A.S., Australian National University, Canberra 2600, Australia
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Synopsis

This note characterises those Banach space valued, scalar-type spectral operators T = ∫ z dP(z), where P is the resolution of the identity for T, whose indefinite spectral integral E→∫EzdP(z) as a set function of the Borel sets of the complex plane is countably additive with respect to the uniform operator topology.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 1-2 , 1985 , pp. 141 - 146
Copyright
Copyright © Royal Society of Edinburgh 1985

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