Similarity and approximation of EP operators

Article Mathematics, Applied

Compact perturbations of Moore-Penrose invertible operators

Boting Jia

Summary: Firstly, the stability of the Moore-Penrose invertibility of Hilbert space operators is studied, establishing necessary and sufficient conditions for the invariance of the Moore-Penrose invertibility under small perturbations, compact perturbations, and small compact perturbations. Secondly, the lifting problem of Moore-Penrose invertible elements of the Calkin algebra is studied, showing that essentially Moore-Penrose invertible operators are small compact perturbations of Moore-Penrose invertible operators. Finally, the compactness of Moore-Penrose spectra is discussed, showing that each Hilbert space operator can be perturbed into an operator with a nonempty compact Moore-Penrose spectrum by an arbitrarily small compact perturbation. (c) 2023 Elsevier Inc. All rights reserved.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2023)

添加到收藏夹

Article Mathematics

Remark on the core-EP pre-order of Hilbert space operators

Xiaoli Deng et al.

Summary: This note provides the necessary and sufficient conditions for the core-EP relation to hold, improving upon the recent results by D. Mosic in Quaestiones Mathematicae.

LINEAR & MULTILINEAR ALGEBRA (2021)

添加到收藏夹

Article Mathematics

WEIGHTED CORE-EP INVERSE AND WEIGHTED CORE-EP PRE-ORDERS IN A C*-ALGEBRA

Dijana Mosic

Summary: This paper extends the weighted core-EP inverse and weighted core-EP pre-orders of bounded linear operators on Hilbert spaces to elements of a C*-algebra, generalizing some properties and proving new ones. By introducing weighted elements, new weighted pre-orders are presented on the set of all wg-Drazin invertible elements of a C*-algebra, leading to the introduction and characterization of new partial orders extending the core-EP pre-order.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY (2021)

添加到收藏夹

Article Mathematics, Applied

Generalization of core-EP inverse for rectangular matrices

Dijana Mosic et al.

Summary: The concept of the g-core-EP inverse extends the well-known core-EP inverse to rectangular matrices using the outer inverse and the Moore-Penrose inverse. Various properties, representations, and characterizations of the g-core-EP inverse are examined. Additionally, the *g-core-EP inverse is introduced and studied as the dual of the g-core-EP inverse, with integral and limit representations also being considered, along with applications in solving restricted systems of linear equations.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

添加到收藏夹

Article Mathematics, Applied