Simultaneous extensions of a family of linear operators
Rodica-Mihaela Dăneţ, Marian-Valentin Popescu, Nicoleta Popescu · Operators and Matrices · 2015
In this paper we study when an arbitrary family of (positive) linear operators, defined on vector subspaces in an ordered vector space E with values in a Dedekind complete ordered vector space F , has a (positive) linear simultaneous extension. Some previous results of the first author concerning the existence of a (positive) linear common extension for two (positive) linear operators are generalized in the line of an appropriate theorem of D. Maharam. The results obtained are related to the classical Mazur-Orlicz theorem and its famous consequence, the Hahn-Banach theorem. Some applications of the main results pertaining to convex analysis, functional analysis and vector measure theory are given.