Mixed-type reverse order law for Moore-Penrose inverse of products of three elements in ring with involution

Abstract

In this paper we establish some results concerning the mixed-type reverse order laws for the Moore-Penrose inverse of various products of three elements in rings with involution.

Mixed-Type Reverse Order Laws for Generalized Inverses over Hilbert Space

“…Let H and K be infinite dimensional Hilbert spaces and ( ) [7] studied the mixed-type reverse-order laws for…”

“…We generalized the results from [7] and [9] to the case of bounded linear operators on Hilbert spaces. Moreover, a new equivalent condition of ( ) …”