Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert C^*-modules

This paper investigates the scenario where two operators share the same range, which has proven to be highly beneficial in practical applications, especially for efficiently computing the Moore-Penrose inverse of specific operators. We establish specific conditions under which the reverse order law holds for Moore-Penrose inverses. Furthermore, we explore the relationship between the ranges and Moore-Penrose inverse of operators involved in a factorization A = BDC within the framework of a Hilbert C^*-module.

Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert C^*-modules Keywords:

Moore-Penrose inverse‎ , ‎Reverse order law , Hilbert C^*-module