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Bouchikhi, Lahcen; El Kinani, Abdellah

The Weyl functional calculus in Michael-algebras. (English) Zbl 1501.46043

Rocky Mt. J. Math. 52, No. 3, 805-816 (2022).
Summary: 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.

MSC:

46H30 Functional calculus in topological algebras
46J05 General theory of commutative topological algebras

Keywords:

Fourier inversion formula; Weyl functional calculus; Michael algebra; Paley-Wiener of \(r\)-exponential type; numerical range; tempered distribution; joint spectrum; P. Lévy’s theorem analog
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References:

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