UBIQUITOUS PROPERTIES OF CERTAIN OPERATIONAL QUANTITIES OF LINEAR RELATIONS IN NORMED SPACES

Abstract

Let X and Y be normed spaces and T a linear relation in X x Y. Certain known operational quantities of linear operators are extended to linear relations. Properties of T such as precompactness, strict singularity, upper semi-Fredholmness and partial continuity are defined and characterised in terms of the given quantities, and certain uniform boundedness properties of these quantities derived.