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FUNCTIONAL CALCULUS EXTENSIONS ON DUAL SPACES

Part of: Special classes of linear operators

Published online by Cambridge University Press:  10 March 2009

VENTA TERAUDS
VENTA TERAUDS*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, University Drive, Callaghan NSW 2308, Australia (email: [email protected])
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Abstract

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In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this result is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply our theorem to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.

Keywords

functional calculusfinitely spectral operatorswell-bounded operatorsAC(σ) operators

MSC classification

Secondary: 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 71 - 77
Copyright
Copyright © Australian Mathematical Society 2009

References

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