Continuous slice functional calculus in quaternionic Hilbert spaces
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)].
scientific article; zbMATH DE number 6204403
scientific article