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Positivity

, Volume 22, Issue 2, pp 461–476 | Cite as

Riesz–Kantorovich formulas for operators on multi-wedged spaces

  • Christopher Schwanke
  • Marten Wortel
Article

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 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.

Keywords

Multi-wedged spaces Multi-lattices Riesz–Kantorovich formulas 

Mathematics Subject Classification

06F20 46A40 

Notes

Acknowledgements

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.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Unit for BMINorth-West UniversityPotchefstroomSouth Africa
  2. 2.Claude Leon FoundationVlaeberg, Cape TownSouth Africa
  3. 3.DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)GautengSouth Africa

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