*Ian
Doust's *i*nformation pages*

## Extensions of an *AC*(σ) functional calculus

*J. Math. Anal. Appl.* **362** (2010), 100-106. [doi:10.1016/j.jmaa.2009.10.001.]
##
Ian Doust and Venta Terauds

**Address:** (ID) School of Mathematics, University of New South Wales, Sydney
NSW 2052, Australia
**Email:** i.doust@unsw.edu.au

**Abstract:**
On a reflexive Banach space $X$, if an operator $T$ admits a functional
calculus for the absolutely continuous functions on its spectrum $\sigma(T)
\subseteq \mathbb{R}$, 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 $L^p$ spaces.

Please contact Ian if you have any trouble downloading the files.