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]
|Titolo:||Slice regular semigroups|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1090/tran/7354|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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