Riesz–Kantorovich formulas for operators on multi-wedged spaces
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 that are 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.
KeywordsMulti-wedged spaces Multi-lattices Riesz–Kantorovich formulas
Mathematics Subject Classification06F20 46A40
This research was partially supported by the Claude Leon Foundation (first author) and by the DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (both authors). Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the CoE-MaSS.