<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We prove Hahn-Banach, sandwich and extension theorems for vector lattice-valued operators, equivariant with respect to a given group <italic>G</italic> 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 <italic>G</italic>.</p></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.

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

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We prove Hahn-Banach, sandwich and extension theorems for vector lattice-valued operators, equivariant with respect to a given group G of homomorphisms. As...

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

Published Online: Nov 04, 2020

Page range: 11 - 34

Received: Feb 18, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0015

Keywords
vector lattice, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem

© 2020 Antonio Boccuto, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Nov 04, 2020

Page range: 11 - 34

Received: Feb 18, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0015

Keywordsvector lattice, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem

© 2020 Antonio Boccuto, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
vector lattice, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem