Journal of Geometric Analysis

, 19:601

On Some Properties of the Quaternionic Functional Calculus

Authors

  • Fabrizio Colombo
    • Dipartimento di MatematicaPolitecnico di Milano
    • Dipartimento di MatematicaPolitecnico di Milano
Article

DOI: 10.1007/s12220-009-9075-x

Cite this article as:
Colombo, F. & Sabadini, I. J Geom Anal (2009) 19: 601. doi:10.1007/s12220-009-9075-x

Abstract

In some recent works we have developed a new functional calculus for bounded and unbounded quaternionic operators acting on a quaternionic Banach space. That functional calculus is based on the theory of slice regular functions and on a Cauchy formula which holds for particular domains where the admissible functions have power series expansions. In this paper, we use a new version of the Cauchy formula with slice regular kernel to extend the validity of the quaternionic functional calculus to functions defined on more general domains. Moreover, we show some of the algebraic properties of the quaternionic functional calculus such as the S-spectral radius theorem and the S-spectral mapping theorem. Our functional calculus is also a natural tool to define the semigroup etA when A is a linear quaternionic operator.

Keywords

Slice regular functionsFunctional calculusSpectral theoryAlgebraic propertiesS-spectral radius theoremS-spectral mapping theoremSemigroup of a linear quaternionic operator

Mathematics Subject Classification (2000)

47A1047A6030G35
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