Local spectral theory for Drazin invertible operators
Let \(X\) be an infinite dimensional complex Banach space and \(L(X)\) denotes the Banach algebra of all bounded linear operators on \(X\). In the present paper, the authors prove that the spectral properties SVEP, property (C), property (Q) and property \((\beta)\) are transferred from a Drazin invertible operator \(R\in L(X)\) to its Drazin inverse \(S\) and, reciprocally, also the spectral properties property \((\delta)\) and decomposability are transferred from a Drazin invertible operator \(R\in L(X)\) to its Drazin inverse \(S\). Among other results, they show that the properties polaroid and a-polaroid are transferred from \(R\in L(X)\) to its Drazin inverse \(S\).
scientific article; zbMATH DE number 6511565
scientific article