- Title
- Functional calculus extensions on dual spaces
- Creator
- Terauds, Venta
- Relation
- Bulletin of the Australian Mathematical Society Vol. 79, Issue 1, p. 71-77
- Publisher Link
- http://dx.doi.org/10.1017/s0004972708001032
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2009
- Description
- 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.
- Subject
- functional calculus; finitely spectral operators; well-bounded operators; AC(σ) operators
- Identifier
- http://hdl.handle.net/1959.13/809201
- Identifier
- uon:7851
- Identifier
- ISSN:0004-9727
- Language
- eng
- Reviewed
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