vix.ing · top · new · best · stats · spec

Operators on anti-dual pairs: Means of positive operators

2026/07/16 by Zsigmond Tarcsay, Ábel Göde
Mathematics · #math.FA #math.OA #msc:47A64 #msc:47B65 #msc:46L30

paper · pdf

30 pages

arxiv created 2026/07/16 · arxiv updated 2026/08/04

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.

Citations