Operators on anti-dual pairs: Supremum and infimum of positive operators

Our purpose in this note is to investigate the order properties of positive operators from a locally convex space into its conjugate dual. We introduce a natural generalization of the Busch-Gudder strength function and we prove Kadison's anti-lattice theorem and Ando's result on the infimum of positive operators in that context.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).

Automated summary

The purpose of this article is to explore the order properties of positive operators, and introduce a natural generalization of the Busch-Gudder strength function in the context of locally convex spaces. We also prove Kadison's anti-lattice theorem and Ando's result on the infimum of positive operators.