Chunyuan Deng

Some results on the generalized Drazin inverse of operator matrices

The generalized Drazin inverse M d of a 2 × 2 operator matrix is considered, where A ∈ ℬ(X) and D ∈ ℬ(Y) are generalized Drazin invertible. Expressions for the generalized Drazin inverse M d of operator matrix M in terms of the individual blocks A, B, C, D, A d and D d are derived under some conditions.

Further results on the Moore–Penrose invertibility of projectors and its applications

The aim of this article is to investigate new results on the Moore–Penrose invertibility of the products and differences of projectors and generalized projectors. The range relations of projectors and the detailed representations for Moore–Penrose inverses are presented.

The Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized projectors

In this paper, some representations for the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors are found. Also, the invertibility for some linear combinations of commuting generalized and hypergeneralized projectors is considered.

Properties of m-EP operators

In this paper, we study the characteristics of m-EP operators and the properties of the particular case of m-EP operators that are Drazin invertible. The relations between the Moore–Penrose inverses and Drazin inverses are built by m-EP and many closely equivalent relations are investigated by using appropriate idempotents.

Characterizations and representations of the (P, Q)-outer generalized inverse

We present a new explicit expression for the (P, Q)-outer generalized inverse based on the idempotent operators P and Q. We derive properties of the (P, Q)-outer generalized inverse and analyse relations among the various (P, Q)-outer generalized inverses.

Invertibility and stability of linear combinations of m-potent operators

In this paper, the stabilities of the nullity, invertibility and generalized invertibility of linear combinations or are investigated, where and be two and potents, respectively.

Expression for the multiplicative perturbation of the Moore–Penrose inverse

Abstract In this paper, we study the multiplicative perturbation of an operator of the form , where X and Y are invertible. Based on this result, we study the Moore–Penrose invertibility of block matrix M with Schur complement having closed range. We recover the cases when a Schur complement in M is either equal to zero or nonsingular. The necessary and sufficient conditions for the existence as well as the expressions for the Moore–Penrose inverses are obtained.

The solutions to some operator equations with corresponding operators not necessarily having closed ranges

ABSTRACT In this paper, we study the solvability of the operator equations in the general setting of infinite-dimensional Hilbert space with corresponding operators no necessarily having closed range. We get the necessary and sufficient conditions for the existences of the solutions and obtain formulae in each case for the general selfadjoint, positive and real positive solutions to these operator systems.

On the invertibility and range closedness of the linear combinations of a pair of projections

The invertibility and range closedness of the linear combinations of a pair of projections for any scalars are investigated.