Riesz-Kantorovich formulas for operators on multi-wedged spaces

TL;DR

This paper generalizes the concepts of suprema and infima to multi-wedged vector spaces, introducing multi-lattices and Riesz-Kantorovich formulas to extend lattice theory to more abstract settings.

Contribution

It introduces multi-suprema, multi-infima, and multi-lattices, extending classical lattice concepts to multi-wedged spaces, and develops Riesz-Kantorovich formulas in this new context.

Findings

Defined multi-suprema and multi-infima for multi-wedged spaces

Introduced the concept of multi-lattices as an abstraction of vector lattices

Derived Riesz-Kantorovich formulas for operators in multi-wedged spaces

Abstract

We introduce the notions of multi-suprema and multi-infima for vector spaces equipped with a collection of wedges, generalizing the notions of suprema and infima in ordered vector spaces. Multi-lattices are vector spaces closed under multi-suprema and multi-infima and are thus an abstraction of vector lattices. The Riesz decomposition property in the multi-wedged setting is also introduced, leading to Riesz-Kantorovich formulas for multi-suprema and multi-infima in certain spaces of operators.