CHARACTERIZATIONS OF INESSENTIAL LINEAR RELATIONS

Abstract

In order to study the inessential operators Tarafdar introduced the notion of improjective operators. Aiena and González characterize the class of inessential operators in more algebraic terms and they also obtain characterizations of the inessential operators among the improjective operators in terms of the complementability of some subspaces. In the present paper, we extend these characterizations to the general case of linear relations. Firstly, we characterize the inessential linear relations by the nullity and the deficiencies. Secondly, we apply such algebraic results to characterize the inessential linear relations among the improjective linear relations in terms of the complementability of some null and range spaces.