Core–EP orthogonal operators

Abstract

The concept of the core orthogonality (CO) was recently introduced for two square matrices A and B of the same size and of index at most 1 as follows: A is core orthogonal to B if and , where is the core inverse of A. Using the core–EP inverse instead of the core inverse, we extend the concept of the CO and present the new concept of the core–EP orthogonality (CEPO) for two Drazin invertible bounded linear Hilbert space operators A and B as follows: A is said to be core–EP orthogonal to B if and , where is the core–EP inverse of A. A number of characterizations for CEPO are presented as well as the relation between the CEPO and core–EP additivity. Applying CEPO, the concept of strong core–EP orthogonality is defined and characterized.