Slice regular semigroups

2016/05/05 by Riccardo Ghiloni, Ghiloni, Riccardo, Vincenzo Recupero +1
Mathematics · #30G35 #47A1 #47A60 #47D03 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:30G35 #msc:47A1 #msc:47A60 #msc:47D03

paper · pdf · doi:10.48550/arxiv.1605.01645

A misprint in the second displayed formula of Definition 6.11 (p. 28) has been corrected

arxiv created 2016/05/17 · arxiv updated 2016/05/19

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.

Related

• Quaternionic analogues of Bers's theorem and Iss'sa's theorem
• Slice regular functions on real alternative algebras
• Power-bounded quaternionic operators
• Algebra of slice regular functions on non-symmetric domains in several quaternionic variables
• On slice regular fractal-fractional Dirichlet type spaces