The Sandwich Theorem for Sublinear and Superlinear Functionals
Abstract
The Hahn-Banach theorem is an extension theorem for linear functionals which preserves certain properties. Specifically, if a linear functional is defined on a subspace of a real vector space which is dominated by a sublinear functional on the entire space, then this functional can be extended to a linear functional on the entire space which is still dominated by a sublinear functional. In this paper, we generalize this result to show that a linear functional defined on a subspace of a real vector space which is dominated by a sublinear functional and also dominates a superlinear functional on the entire space can be extended to a linear functional on the entire space which is also dominated by a sublinear functional and dominates a superlinear functional.
Cite
@article{arxiv.1611.02670,
title = {The Sandwich Theorem for Sublinear and Superlinear Functionals},
author = {A. T. Diab and S. I. Nada and D. L. Fearnley},
journal= {arXiv preprint arXiv:1611.02670},
year = {2016}
}