AI 中文总结
本文发展反对偶对上正算子的Kubo-Ando型均值理论，扩展经典算子均值框架，引入Busch-Gudder型强度函数并研究其与均值的相互作用，还将理论应用于希尔伯特空间算子等对象。
AI 中文摘要
我们发展了反对偶对上正算子的Kubo-Ando型均值理论，该框架将经典算子均值理论扩展到有界希尔伯特空间算子之外，为非半双线性型和C*-代数上的态等多种具体正对象类提供了统一框架。我们还引入了反对偶对上正算子的Busch-Gudder型强度函数，并研究其与算子均值的相互作用，将该理论应用于希尔伯特空间算子、非负型及可表示正泛函。
英文摘要
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.
Comments30 pages
