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Journal of Mathematical Sciences

, Volume 239, Issue 5, pp 654–705 | Cite as

Topological Algebras of Measurable and Locally Measurable Operators

  • M. A. MuratovEmail author
  • V. I. Chilin
Article
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Abstract

In this paper, we review the results on topological ∗-algebras S(M), S(M, τ), and LS(M) of measurable, τ -measurable, and locally measurable operators affiliated with the von Neumann algebra M. Also, we consider relations between those algebras for different classes of von Neumann algebras and establish the continuity of operator-valued functions with respect to the local convergence in measure. We describe maximal commutative ∗-subalgebras of the algebra LS(M) as well.

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Authors and Affiliations

  1. 1.V. I. Vernadsky Crimean Federal UniversitySimferopolRussia
  2. 2.M. Ulugbek National University of UzbekistanTashkentUzbekistan

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