Functional calculus extensions on dual spaces

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

		Thumbnail	File	Description	Size	Format