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Some new perturbation results on left and right generalized Drazin invertible operators. (English) Zbl 07274322

A bounded linear operator over a complex Banach space is said to be left (right) generalized Drazin invertible, if zero is not an accumulation point of its approximate point spectrum (surjectivity spectrum). It is called generalized Drazin invertible, if it is both left and right generalized Drazin invertible. The authors investigate the stability of these three classes of generalized Drazin invertible operators, under quasinilpotent, power finite rank, compact and Riesz commuting perturbations. A description of the largest open subset contained in the space of each of these three classes of operators.

MSC:

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A55 Perturbation theory of linear operators
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47B07 Linear operators defined by compactness properties
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