Operators on anti-dual pairs

Tarcsay, Zsigmond ORCID: https://orcid.org/0000-0001-8102-5055 and Göde, Ábel (2024) Operators on anti-dual pairs. Journal of Mathematical Analysis and Applications, 531 (2P2). DOI https://doi.org/10.1016/j.jmaa.2023.127893

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Official URL: https://doi.org/10.1016/j.jmaa.2023.127893

Abstract

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.

Item Type:

Article

Uncontrolled Keywords:

positive operator, anti-dual pair, supremum infimum, Lebesgue decomposition, strength function

Divisions:

Institute of Data Analytics and Information Systems

Subjects:

Mathematics, Econometrics

DOI:

https://doi.org/10.1016/j.jmaa.2023.127893

ID Code:

9510