Topologies on central extensions of von Neumann algebras
Shavkat AyupovDepartment of Algebra and Analysis, Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Dormon Yoli str., 29, Tashkent, 100125, UzbekistanKarimbergen KudaybergenovKarakalpak State UniversityR. T. DjumamuratovKarakalpak State University
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Аннотация
Abstract Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.
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