Slice regular semigroups
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- by Riccardo Ghiloni and Vincenzo Recupero PDF
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Abstract:
In this paper we introduce the notion of slice regular right linear semigroup in a quaternionic Banach space. It is an operatorial function which is slice regular (a noncommutative counterpart of analyticity) and which satisfies a noncommutative semigroup law characterizing the exponential function in an infinite dimensional noncommutative setting. We prove that a right linear operator semigroup in a quaternionic Banach space is slice regular if and only if its generator is spherical sectorial. This result provides a connection between the slice regularity and the noncommutative semigroups theory and characterizes those semigroups which can be represented by a noncommutative Cauchy integral formula. All our results are generalized to Banach two-sided modules having as a set of scalar any real associative *-algebra, Clifford algebras $\mathbb {R}_n$ included.References
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Additional Information
- Riccardo Ghiloni
- Affiliation: Dipartimento di Matematica, UniversitĂ di Trento, Via Sommarive 14, 38123 Trento, Italy
- MR Author ID: 699436
- Email: ghiloni@science.unitn.it
- Vincenzo Recupero
- Affiliation: Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
- MR Author ID: 692450
- Email: vincenzo.recupero@polito.it
- Received by editor(s): November 4, 2016
- Published electronically: March 20, 2018
- Additional Notes: The first author was partially supported by INFN-TIFPA and by GNSAGA of INdAM
The second author was a member of GNAMPA of INdAM - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 4993-5032
- MSC (2010): Primary 30G35, 47D03, 47A60, 47A10
- DOI: https://doi.org/10.1090/tran/7354
- MathSciNet review: 3787379