On the formulations of the quaternionic functional calculus
type: Item
instance of: scholarly article
title: On the formulations of the quaternionic functional calculus
zbMATH Open document ID: 1220.47022
author: Fabrizio Colombo
author: Irene Sabadini
published in: Journal of Geometry and Physics
publication date: 2010-08-19T00:00:00Z
review text: In [\textit{F. Colombo} and \textit{I. Sabadini}, J. Geom. Anal. 19, No.~3, 601--627 (2009; Zbl 1166.47018)], the authors developed a functional calculus for right linear quaternionic operators that enjoys many properties similar to those of the Riesz-Dunford calculus. In the paper under review, a functional calculus for left linear quaternionic operators on bilateral quaternionic Banach spaces is introduced and a comparative study of these calculi is performed. The basic ingredients are the left and the right S-resolvents associated to any quaternionic operator. Several algebraic and analytic properties of this calculus are proved, including a spectral mapping theorem. Bounded perturbations for the resolvents are also studied.
reviewed by: Bebe Prunaru
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 5773070
zbMATH Keywords: left and right linear operators
zbMATH Keywords: Cauchy formula for right slice regular functions
zbMATH Keywords: quaternionic functional calculus
zbMATH Keywords: closed linear operators
zbMATH Keywords: \(S\)-resolvent operator
zbMATH Keywords: \(S\)-spectrum
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.05.014
OpenAlex ID: W2021255261
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DOI: 10.1016/J.GEOMPHYS.2010.05.014
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description: scientific article; zbMATH DE number 5773070