In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the new notion of slice-regularity, see Gentili and Struppa (Acad Sci Paris 342:741–744, 2006) and the key tools are a new resolvent operator and a new eigenvalue problem.
Non commutative functional calculus: bounded operators / Colombo, Fabrizio; Gentili, Graziano; Sabadini, Irene; Struppa, Daniele C.. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - STAMPA. - 4:(2010), pp. 821-843. [10.1007/s11785-009-0015-3]
Non commutative functional calculus: bounded operators
GENTILI, GRAZIANO;
2010
Abstract
In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the new notion of slice-regularity, see Gentili and Struppa (Acad Sci Paris 342:741–744, 2006) and the key tools are a new resolvent operator and a new eigenvalue problem.
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