One-sided core–EP orthogonal operators
Olivera Stanimirović, Dijana Mosić · Linear and Multilinear Algebra · 2025
The concepts of the left and right core–EP orthogonal operators are introduced as one-sided versions of core–EP orthogonal operators and as generalizations of left and right core orthogonal operators. We present the properties and characterizations of left and right core–EP orthogonality, as well as the operator matrix forms of left and right core–EP orthogonal operators. We also study the additivity of the core–EP inverse under one-sided core–EP orthogonality of adequate operators. Consequently, we recover some known properties and introduce several new ones related to left and right core orthogonal operators.