Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras
Volume 167 / 2005
Studia Mathematica 167 (2005), 219-226
MSC: 47A60, 47A10, 46H30.
DOI: 10.4064/sm167-3-3
Abstract
We investigate the weak spectral mapping property (WSMP) $$ \overline {\widehat {\mu }(\sigma (A))}=\sigma (\widehat {\mu }(A)), $$ where $A$ is the generator of a ${\mathcal C}_0$-semigroup in a Banach space $X $, $\mu $ is a measure, and $\widehat {\mu }(A)$ is defined by the Phillips functional calculus. We consider the special case when $X$ is a Banach algebra and the operators $e^{At}$, $t\geq 0,$ are multipliers.
