Riesz-Kantorovich formulas for operators on multi-wedged spaces

Christopher Schwanke, Marten Wortel

Published 2016-09-19Version 1

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.