Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras

Volume 167 / 2005

Eva Fašangová, Pedro J. Miana Studia Mathematica 167 (2005), 219-226 MSC: 47A60, 47A10, 46H30. DOI: 10.4064/sm167-3-3


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.


  • Eva FašangováDepartment of Mathematical Analysis
    Charles University
    Sokolovská 83
    186 75 Praha, Czech Republic
  • Pedro J. MianaDepartment of Mathematics
    Universidad de Zaragoza
    50009 Zaragoza, Spain

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image