Topologies on central extensions of von Neumann algebras
Shavkat AyupovThe Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, Trieste, 34151, ItalyKarimbergen KudaybergenovKarakalpak State UniversityR. T. DjumamuratovKarakalpak State University
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Annotatsiya
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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