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Well-bounded operators of type (B) in a class of Banach spaces

Published online by Cambridge University Press:  09 April 2009

Werner Ricker
Werner Ricker
Affiliation:
Centre for Mathematical AnalysisAustralian National UniversityCanberra, 2600, Australia
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Abstract

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It is shown that in a Grothendieck space with the Dunford-Pettis property, the class of well-bounded operators of type (B) coincides with the class of scalar-type spectral operators with real spectrum. It turns out that in such Banach spaces, analogues of the classical theorems of Hille-Sz. Nagy and Stone concerned with the integral representation of C0-semigroups of normal operators and strongly continuous unitary groups in Hilbert spaces, respectively, are of a very special nature.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 399 - 408
Copyright
Copyright © Australian Mathematical Society 1987

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