Geodesic
Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras
Eva Fašangová1 ; Pedro J. Miana2
1Department of Mathematical Analysis Charles University Sokolovská 83 186 75 Praha, Czech Republic
2Department of Mathematics Universidad de Zaragoza 50009 Zaragoza, Spain
Studia Mathematica, Tome 167 (2005) no. 3, pp. 219-226
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm167-3-3
Keywords: investigate weak spectral mapping property wsmp overline widehat sigma sigma widehat where generator mathcal semigroup banach space measure widehat defined phillips functional calculus consider special banach algebra operators geq multipliers

Eva Fašangová  1   ; Pedro J. Miana  2

1 Department of Mathematical Analysis Charles University Sokolovská 83 186 75 Praha, Czech Republic
2 Department of Mathematics Universidad de Zaragoza 50009 Zaragoza, Spain 
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Eva Fašangová; Pedro J. Miana. Spectral mapping inclusions for the Phillips functional
 calculus in Banach spaces and algebras. Studia Mathematica, Tome 167 (2005) no. 3, pp. 219-226. doi: 10.4064/sm167-3-3

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