UM
The H∞ functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators
Daniel Alpay1; Fabrizio Colombo2; Tao Qian3; Irene Sabadini2
2016-09-15
Source PublicationJournal of Functional Analysis
ISSN10960783 00221236
Volume271Issue:6Pages:1544-1584
Abstract

In this paper we extend the H functional calculus to quaternionic operators and to n-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called S-functional calculus. The S-functional calculus has two versions: one for quaternionic-valued functions and one for Clifford algebra-valued functions and can be considered the Riesz–Dunford functional calculus based on slice hyperholomorphicity, because it shares with it the most important properties. The S-functional calculus is based on the notion of S-spectrum which, in the case of quaternionic normal operators on a Hilbert space, is also the notion of spectrum that appears in the quaternionic spectral theorem. The main purpose of this paper is to construct the H functional calculus based on the notion of S-spectrum for both quaternionic operators and for n-tuples of noncommuting operators. We remark that the H functional calculus for (n+1)-tuples of operators applies, in particular, to the Dirac operator.

KeywordH∞ Functional Calculus N-tuples Of Noncommuting Operators Quaternionic Operators S-spectrum
DOI10.1016/j.jfa.2016.06.009
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000381233000005
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Cited Times [WOS]:17   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorFabrizio Colombo
Affiliation1.Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
2.Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy
3.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macao, China
Recommended Citation
GB/T 7714
Daniel Alpay,Fabrizio Colombo,Tao Qian,et al. The H∞ functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators[J]. Journal of Functional Analysis,2016,271(6):1544-1584.
APA Daniel Alpay,Fabrizio Colombo,Tao Qian,&Irene Sabadini.(2016).The H∞ functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators.Journal of Functional Analysis,271(6),1544-1584.
MLA Daniel Alpay,et al."The H∞ functional calculus based on the S-spectrum for quaternionic operators and for n-tuples of noncommuting operators".Journal of Functional Analysis 271.6(2016):1544-1584.
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