Hahn-Banach and Sandwich Theorems for Equivariant Vector Lattice-Valued Operators and Applications

Boccuto, Antonio

doi:10.2478/tmmp-2020-0015

Abstract

We prove Hahn-Banach, sandwich and extension theorems for vector lattice-valued operators, equivariant with respect to a given group G of homomorphisms. As applications and consequences, we present some Fenchel duality and separation theorems, a version of the Moreau-Rockafellar formula and some Farkas and Kuhn-Tucker-type optimization results. Finally, we prove that the obtained results are equivalent to the amenability of G.

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Hahn-Banach and Sandwich Theorems for Equivariant Vector Lattice-Valued Operators and Applications

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