This article examines a way to define left and right versions of the large class of “(b, c)-
inverses” introduced by the writer in (2012)[6]: Given any semigroup S and any a, b, c∈ S …

Let R denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm
operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder …

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index
of a B-Fredholm operator. This concept will be used to extend some known results in …

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 …

In\cite {koliha}, Koliha proved that $ T\in L (X) $($ X $ is a complex Banach space) is
generalized Drazin invertible operator equivalent to there exists an operator $ S …

In this paper, we are interested in the perturbation of generalized Drazin operators by
compact, polynomially compact and polynomially Riesz operators. We show that the …

We investigate the perturbation problems of left and right generalized Drazin invertibility of
bounded linear operators on Hilbert spaces. Some algebraic and topological …

This paper initiates a study of upper and lower generalized Drazin invertible linear relations
classes. We first aim to give a characterization of these classes via a generalized Kato …

In this paper, we define and study the pseudo upper and lower semi B-Fredholm of bounded
operators in a Banach space. In particular, we prove equality up to $ S (T) $ between the left …

Upper and lower generalized Drazin invertible operators were introduced in [5]. We will
characterize these operators and their properties will be studied. In addition, we make …