The Weyl functional calculus in Michael-algebras

Abstract

We define and study a Weyl functional calculus for an n-tuple of commuting Paley–Wiener of r-exponential type elements of a Michael algebra. We show that this calculus preserves the same properties as in the Banach case. In particular, it is well defined for polynomials and gives results consistent with the natural algebraic definition. As applications, we obtain for bounded real numerical range series, two generalizations of P. Lévy theorems: the first one for Fourier series and the second for power series.