Necessary conditions for existence of majorized extensions of continuous linear operators (Q2366413)

The present note is a continuation of some previous researches of the author, related to the simultaneous extension of a family of operators majorized by a fixed sublinear operator, all having values in an ordered vector space \(V\), and some intrinsic properties of the space \(V\). Prior results showed that the conditional completeness of \(V\) is equivalent to the stated extension property. Here the author proves that the same condition is equivalent to an interpolation property of \(V\) with respect to pairs of subsets.