*-subalgebras of locally measurable operators affiliated to a von Neumann algebra

Abstract:
The *-algebras measurable operators $S(M)$,  $\tau$ is measurable operators $S(M,\tau)$ and locally measurable operators $LS(M)$, affiliated to a von Neumann algebras $M$ are considered. The von Neumann algebra $M$ is a *-subalgebra of $S(M,\tau)$, $S(M)$ and $LS(M)$, and coincides with the set of all bounded operators of this algebras. $M \subset S(M,\tau) \subset \cup_\tau  S(M,\tau )\subset  S(M)\subset  LS(M)$. Terms over are brought when these algebras coincide and when they are different.