Left and right-Drazin inverses in rings and operator algebras
Yanxun Ren, Lining Jiang
Abstract
The paper introduces the left and right versions of the large class of Drazin inverses in terms of the left and right annihilators in a ring, which are called left-Drazin and right-Drazin inverses. We characterize some basic properties of these one-sided Drazin inverses, and discuss Jacobson’s lemma for them. In addition, the relation between the Drazin inverses and these two one-sided inverses is given by means of the spectrum and the operator decomposition. As an application, the left-Drazin and right-Drazin invertibilities in the Calkin algebra are investigated.
Topics & Concepts
MathematicsDrazin inversePure mathematicsRing (chemistry)Spectrum (functional analysis)Algebra over a fieldGeometryOrganic chemistryInversePhysicsChemistryQuantum mechanicsMatrix Theory and AlgorithmsAdvanced Topics in AlgebraControl and Stability of Dynamical Systems