SUBLINEAR OPERATORS BETWEEN BANACH LATTICES

Abstract

A class of sublinear operators between Banach lattices E and F are characterized when E and F have representations as extended real-valued functions on X and Y, respectively. It is shown that T is M-sublinear if and only if T is related to a weighted supremum over X, i.e., Tf(y) is related to V r(z, y)f(x) for f ≥ 0 in E and r a real-valued function on X x Y. This is used to study finite conditions on the weighting function r.