An equational approach to products of relatively regular operators

A bounded linear operatorT on Banach spaceX is called relatively regular if its nullspaceN(T) and rangeR(T) are closed complemented subspaces ofX. It is known that the product of two relatively regular operators is not necessarily relatively regular. This paper shows how to find conditions, more general than those previously known, to ensure that two relatively regular operators have relatively regular product.This work was supported in part by NRC Operating Grant A3985 and Canada Council Leave Fellowship.