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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 167 / 2005

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

#### Streszczenie

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.

#### Autorzy

• Eva FašangováDepartment of Mathematical Analysis
Charles University
Sokolovská 83
186 75 Praha, Czech Republic
e-mail
• Pedro J. MianaDepartment of Mathematics