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arXiv · 1611.02670

The Sandwich Theorem for Sublinear and Superlinear Functionals

A. T. Diab·S. I. Nada·D. L. Fearnley
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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.

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A. T. Diab, S. I. Nada, D. L. Fearnley. 2016-11-08. The Sandwich Theorem for Sublinear and Superlinear Functionals. https://arxiv.org/abs/1611.02670

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