Extensions of an AC(σ) functional calculus

Title: Extensions of an AC(σ) functional calculus
Creator: Doust, Ian; Terauds, Venta
Relation: Journal of Mathematical Analysis and Applications Vol. 362, Issue 1, p. 100-106
Publisher Link: http://dx.doi.org/10.1016/j.jmaa.2009.10.001
Publisher: Elsevier
Resource Type: journal article
Date: 2010
Description: On a reflexive Banach space X, if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T)⊆ℝ, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an AC functional calculus is possible for operators acting on families of interpolation spaces such as the Lᵖ spaces.
Subject: functional calculus; well-bounded operators; AC(σ) operators
Identifier: uon:9683
Identifier: http://hdl.handle.net/1959.13/923214
Identifier: ISSN:0022-247X
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