Hahn-Banach and sandwich theorems for equivariant vector lattice-valued operators and applications

Abstract

We prove Hahn-Banach, sandwich and extension theorems

for vector lattice-valued operators, equivariant with respect to a given group $G$ of homo-morphisms. 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 $G$.