New Results on Semiclosed Linear Relations

Abstract

This paper has triple main objectives. The first objective is an analysis ofsome auxiliary results on closedness and boundednes of linear relations. The seconde objective is to provide some new characterization results on semiclosed linear relations. Here it is shown that the class of semiclosed linear relations is invariant under finite and countable sums, products, and limits. We obtain some fundamental new results as well as a Kato Rellich Theorem for semiclosed linear relations and essentially interesting generalizations. The last objective concern semiclosed linear relation with closed range, where we have particularly established new characterizations of closable linear relation.