Core invertibility of operators from the algebra generated by two orthogonal projections

Abstract A Hilbert space operator is said to be core invertible if it has an inner inverse whose range coincides with the of and null adjoint . This notion was introduced by Baksalary, Trenkler, Rakić, Dinčić, Djordjević in last decade, who also proved that invertibility equivalent group inverses coincide only a so-called EP operator. The present paper contains criteria for property as well formulas operators von Neumann algebra generated two orthogonal projections.