Continuous slice functional calculus in quaternionic Hilbert spaces (Q2846889)
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scientific article; zbMATH DE number 6204403
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Continuous slice functional calculus in quaternionic Hilbert spaces |
scientific article; zbMATH DE number 6204403 |
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3 September 2013
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functional calculus
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quaternionic Hilbert space
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slice regular functions
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slice continuous functions
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Continuous slice functional calculus in quaternionic Hilbert spaces (English)
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The authors develop functional calculus of normal operators on quaternionic Hilbert spaces based on the notion of slice continuous functions, extending the earlier concept of slice regular functions (see \textit{G. Gentili} and \textit{D. C. Struppa} [Adv. Math. 216, No. 1, 279--301 (2007; Zbl 1124.30015)]; \textit{R. Ghiloni} and \textit{A. Perotti} [Adv. Math. 226, No. 2, 1662--1691 (2011; Zbl 1217.30044)]). This notion makes it possible to introduce suitable classes of real, complex, and quaternionic \(C^*\)-algebras and to define for each of them a functional calculus for quaternionic bounded normal operators, including spectral mapping properties. For slice regular functions, the above functional calculus agrees with the earlier one in [\textit{F. Colombo, I. Sabadini} and \textit{D. Struppa}, Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions. Basel: Birkhäuser (2011; Zbl 1228.47001)].
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