Non-commutative functional calculus: Unbounded operators |
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| Authors: | Fabrizio Colombo Graziano Gentili Irene Sabadini Daniele C. Struppa |
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| Affiliation: | 1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9 20133 Milano, Italy;2. Dipartimento di Matematica, Universitá di Firenze, Viale Morgagni, 67 A, Firenze, Italy;3. Department of Mathematics and Computer Sciences, Chapman University, Orange, CA 92866, USA |
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| Abstract: | In a recent work, Colombo (in press) [1], we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from the above-mentioned work can be extended to the unbounded case, and we highlight the crucial differences between the two cases. In particular, we deduce a new eigenvalue equation, suitable for the construction of a functional calculus for operators whose spectrum is not necessarily real. |
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| Keywords: | 47A10 47A60 30G35 |
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