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Non Commutative Functional Calculus: Bounded Operators

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133, Milan, Italy

    Fabrizio Colombo & Irene Sabadini

  2. Dipartimento di Matematica, Universitá di Firenze, Viale Morgagni, 67 A, Florence, Italy

    Graziano Gentili

  3. Department of Mathematics and Computer Sciences, Chapman University, Orange, CA, 92866, USA

    Daniele C. Struppa

Authors
  1. Fabrizio Colombo
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  2. Graziano Gentili
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  3. Irene Sabadini
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  4. Daniele C. Struppa
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Corresponding author

Correspondence to Irene Sabadini.

Additional information

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

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