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arXiv · 1605.01645

Slice regular semigroups

Riccardo Ghiloni·Vincenzo Recupero
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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 R_n algebras included.

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Riccardo Ghiloni, Vincenzo Recupero. 2016-05-05. Slice regular semigroups. https://arxiv.org/abs/1605.01645

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