The structures and properties of some generalized invertible operators

ABSTRACT

In this paper, we analyse the matrix structures of various generalized inverses, suggest their applicable scopes and build their relationships with particular projections. As applications, several equivalent conditions for core–EP (Range-Hermitian) relation, star order, sharp order and MP–Core–EP (MPCEP) relation are presented. The relationships among these orders or relations are built. In addition, we introduce some conditions for which the core–EP invertible operators satisfy the reverse order law.

Keywords:

• Core–EP operator
• order
• block-operator matrix

2000 Mathematics Subject Classifications:

• 15A09
• 47A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China under grant number 11671261 and by the Innovation Project of Graduate School of South China Normal University.