Operator factorization of range space relations

TL;DR

This paper investigates the conditions under which operators can be factored through range space relations in Hilbert spaces, providing a characterization of such factorizations.

Contribution

It offers a new theoretical framework for understanding operator factorizations involving range space relations in Hilbert spaces.

Findings

Characterization of operator factorizations in Hilbert spaces

Conditions for the existence of operators satisfying A=BT or A=TB

Advances in the theory of range space relations

Abstract

Given two range space relations A and B in Hilbert spaces, we characterize the existence of a range space operator T such that A = BT, respectively A = TB.