Functional calculus extensions on dual spaces

Details Functional calculus extensions on dual spaces Functional calculus extensions on dual spaces

2008-04-22

arxiv.org/abs/0804.3451v1

Mathematics

Functional Analysis

7 pages

Scientific paper

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 is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.

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