$(o)$-Topology in *-algebras of locally measurable operators

• Date: 2009
• Main Authors: Muratov, M. A., Chilin, V. I., Муратов, M. A, Чилин, В. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3119
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the topology \( t\left( \mathcal{M} \right) \) of convergence locally in measure in the *-algebra \( LS\left( \mathcal{M} \right) \) of all locally measurable operators affiliated to the von Neumann algebra \( \mathcal{M} \). We prove that \( t\left( \mathcal{M} \right) \) coincides with...