On the formulations of the quaternionic functional calculus (Q988903)

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.