谱Stieltjes型积分及其应用
Spectral Stieltjes-Type Integration and Some Applications
摘要：
本文给出了算子值函数关于谱族的Stieltjes型积分。建立了与某些类谱族相关的黎曼-斯蒂尔切斯积分之间的关系，特别是与巴拿赫空间的斯通表示定理有关的谱族。所开发的方法适用于与满足广义Stone定理的单参数表示交换的算子的结构分析。
英文摘要：
This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular, those that arise in the context of the Stone representation theorem for Banach spaces is established. The developed approach is applied to the structural analysis of the operators commuting with a one-parameter representation satisfying the Generalized Stone theorem.
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