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arXiv · 2608.00031

Operators on anti-dual pairs: Means of positive operators

Zsigmond Tarcsay·Ábel Göde
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Abstract

We develop a theory of Kubo-Ando type means for positive operators on anti-dual pairs. This framework extends the classical theory of operator means beyond bounded Hilbert space operators and provides a common setting for several concrete classes of positive objects, including nonnegative sesquilinear forms and states on $C^*$-algebras. We also introduce a Busch-Gudder type strength function for positive operators on anti-dual pairs and investigate its interaction with operator means. Applications are given to Hilbert space operators, nonnegative forms, and representable positive functionals.

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Zsigmond Tarcsay, Ábel Göde. 2026-07-16. Operators on anti-dual pairs: Means of positive operators. https://arxiv.org/abs/2608.00031

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