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Integration maps and local equicontinuity of spectral measures

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

S. Okada  and
W. J. Ricker
W. J. Ricker
Affiliation:
School of Mathematics University of New South Wales Sydney, NSW 2052Australia e-mail: [email protected] e-mail: [email protected]
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Abstract

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One of the useful features of spectral measures which happen to be equicontinuous is that their associated integration maps are bicontinuous isomorphisms of the corresponding L1-space onto their ranges. It is shown here that equicontinuity is not necessary for this to be the case; a somewhat weaker property suffices. This is of some interest in practice since there are many natural examples of spectral measures which fail to be equiconontinuous.

MSC classification

Secondary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 176 - 186
Copyright
Copyright © Australian Mathematical Society 2000

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