Riesz–Kantorovich formulas for operators on multi-wedged spaces |
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Authors: | Christopher Schwanke Marten Wortel |
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Institution: | 1.Unit for BMI,North-West University,Potchefstroom,South Africa;2.Claude Leon Foundation,Vlaeberg, Cape Town,South Africa;3.DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),Gauteng,South Africa |
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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. |
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