2018
Том 70
№ 1

# Muratov M. A.

Articles: 2
Article (Russian)

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

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1531-1540

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 the (o)-topology in $L{S_h}\left( \mathcal{M} \right) = \left\{ {T \in LS\left( \mathcal{M} \right):T* = T} \right\}$ if and only if the algebra $\mathcal{M}$ is σ-finite and is of finite type. We also establish relations between $t\left( \mathcal{M} \right)$ and various topologies generated by a faithful normal semifinite trace on $\mathcal{M}$.

Article (Russian)

### Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1196-1205

We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence are equivalent if and only if the von Neumann algebra is of the type I.