Continuous slice functional calculus in quaternionic Hilbert spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1291.47008
DOI: 10.1142/S0129055X13500062
author: Riccardo Ghiloni
author: Valter Moretti
author: Alessandro Perotti
published in: Reviews in Mathematical Physics
publication date: 2013-09-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.0666
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 81R15
zbMATH DE Number: 6204403
zbMATH Keywords: functional calculus
zbMATH Keywords: quaternionic Hilbert space
zbMATH Keywords: slice regular functions
zbMATH Keywords: slice continuous functions
MaRDI profile type: Publication
arXiv ID: 1207.0666
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OpenAlex ID: W3103599540
title: Continuous slice functional calculus in quaternionic Hilbert spaces
review text: 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)].
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6204403