Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
Copyright policy )Semigroups over real alternative *-algebras: Generation theorems and spherical sectorial operators
The aim of this paper is twofold. On one hand, generalizing some recent results obtained in the quaternionic setting, but using simpler techniques, we prove the generation theorems for semigroups in Banach spaces whose set of scalars belongs to the class of real alternative *-algebras, which includes, besides real and complex numbers, quaternions, octonions and Clifford algebras. On the other hand, in this new general framework, we introduce the notion of spherical sectorial operator and we prove that a spherical sectorial operator generates a semigroup that can be represented by a Cauchy integral formula. It follows that such a semigroup is analytic in time.
29 pages; to appear in Transactions of the American Mathematical Society; formula (1.1) has been corrected
- Polytechnic University of Turin Italy
- University of Trento Italy
Functional calculus for linear operators, quaternions, semigroups of linear operators, Functions of hypercomplex variables; Functional calculus; Semigroups of linear operators; Spectrum; resolvent, real alternative *-algebras, Functional Analysis (math.FA), Mathematics - Functional Analysis, Groups and semigroups of linear operators, octonions, Functions of hypercomplex variables and generalized variables, FOS: Mathematics, Spectrum, resolvent, Functions of hypercomplex variables, functional calculus, semigroups of linear operators, spectrum, resolvent., 30G35, 47D03, 47A60, 47A10
Functional calculus for linear operators, quaternions, semigroups of linear operators, Functions of hypercomplex variables; Functional calculus; Semigroups of linear operators; Spectrum; resolvent, real alternative *-algebras, Functional Analysis (math.FA), Mathematics - Functional Analysis, Groups and semigroups of linear operators, octonions, Functions of hypercomplex variables and generalized variables, FOS: Mathematics, Spectrum, resolvent, Functions of hypercomplex variables, functional calculus, semigroups of linear operators, spectrum, resolvent., 30G35, 47D03, 47A60, 47A10
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