On a theorem of Vesentini

Gerd Herzog¹ ; Christoph Schmoeger¹

¹ Mathematisches Institut I Universität Karlsruhe D-76128 Karlsruhe, Germany

Studia Mathematica, Tome 162 (2004) no. 2, pp. 183-193

Résumé

Let ${\mathcal A}$ be a Banach algebra over ${\mathbb C}$ with unit ${\bf 1}$ and $f: {\mathbb C} \to {\mathbb C}$ an entire function. Let ${\bf f}: {\mathcal A} \to {\mathcal A}$ be defined by $$ {\bf f} (a)={f}(a) \hskip 1em (a\in {\mathcal A}), $$ where $f(a)$ is given by the usual analytic calculus. The connections between the periods of $f$ and the periods of ${\bf f}$ are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of ${\bf f}$, for example in $C^\ast $-algebras.

Détail

DOI : 10.4064/sm162-2-6

Keywords: mathcal banach algebra mathbb unit mathbb mathbb entire function mathcal mathcal defined hskip mathcal where given usual analytic calculus connections between periods periods settled theorem nbsp vesentini proof theorem investigate further properties periods example ast algebras