Pusz--Woronowicz's functional calculus revisited

Pusz--Woronowicz functional calculus and extended operator convex perspectives

In this article, we first study, in the framework of operator theory, Pusz and Woronowicz's functional calculus for pairs of bounded positive operators on Hilbert spaces associated with a homogeneous two-variable function on $[0,\infty)^2$. Our construction has special features that functions on $[0,\infty)^2$ are assumed only locally bounded from below and that the functional calculus is allowed to take extended semibounded self-adjoint operators. To analyze convexity properties of the functional calculus, we extend the notion of operator convexity for real functions to that for functions wit…

重新审视正算子的 Lebesgue 分解

Lebesgue decomposition for positive operators revisited

本文利用 Pusz–Woronowicz 泛函演算思想重新梳理 Ando 的 Hilbert 空间正算子 Lebesgue 分解理论，并重建其核心基础。