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 R_n included.

Slice regular semigroups / Ghiloni, Riccardo; Recupero, Vincenzo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 370:7(2018), pp. 4993-5032. [10.1090/tran/7354]

Slice regular semigroups

Ghiloni, Riccardo;
2018-01-01

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 R_n included.
2018
7
Ghiloni, Riccardo; Recupero, Vincenzo
Slice regular semigroups / Ghiloni, Riccardo; Recupero, Vincenzo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 370:7(2018), pp. 4993-5032. [10.1090/tran/7354]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/224536
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