Factorizations of Linear Relations

TL;DR

This paper characterizes when linear relations can be factored through other relations, extending classical results and providing new insights into the structure of linear relations.

Contribution

It introduces new conditions for the existence of factorizations of linear relations, generalizing and improving upon previous theorems by Douglas and Sebestyén.

Findings

Characterization of factorizations of linear relations

Extension of Douglas and Sebestyén's results

Conditions for the existence of linear relation operators

Abstract

Given two linear relations $A$ and $B$ we characterize the existence of a linear relation (operator) $C$ such that $A\subseteq BC$, respectively $A\subseteq CB.$ These factorizations extend and improve well-known results by R.G. Douglas and Z. Sebesty\'en.