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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Adler S.: Quaternionic Quantum Field Theory. Oxford University Press, New York (1995)
Colombo F., Sabadini I., Sommen F., Struppa D.C.: Analysis of Dirac Systems and Computational Algebra. Progress in Mathematical Physics, vol. 39. Birkhäuser, Boston (2004)
Colombo F., Sabadini I., Struppa D.C.: A new functional calculus for noncommuting operators. J. Funct. Anal. 254, 2255–2274 (2008)
Dunford N., Schwartz J.: Linear Operators, Part I: General Theory. Wiley, New York (1988)
Gentili G., Struppa D.C.: A new approach to Cullen-regular functions of a quaternionic variable. C.R. Acad. Sci. Paris 342, 741–744 (2006)
Gentili G., Struppa D.C.: A new theory of regular functions of a quaternionic variable. Adv. Math. 216, 279–301 (2007)
Jefferies B.: Spectral Properties of Noncommuting Operators. Lecture Notes in Mathematics, 1843. Springer-Verlag, Berlin (2004)
Rudin W.: Functional Analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg (1973)
Stoppato, C.: Poles of regular quaternionic functions. Complex Var. Elliptic Equ. (2009) (in press)
Taylor J.L.: The analytic-functional calculus for several commuting operators. Acta Math. 125, 1–38 (1970)
Taylor J.L.: Functions of several noncommuting variables. Bull. Amer. Math. Soc. 79, 1–34 (1973)
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Communicated by Frank Sommen.
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Colombo, F., Gentili, G., Sabadini, I. et al. Non Commutative Functional Calculus: Bounded Operators. Complex Anal. Oper. Theory 4, 821–843 (2010). https://doi.org/10.1007/s11785-009-0015-3
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DOI: https://doi.org/10.1007/s11785-009-0015-3