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Topologies on central extensions of von Neumann algebras |
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| Authors: | Shavkat A. Ayupov Karimbergen K. Kudaybergenov Rauaj T. Djumamuratov |
| Affiliation: | 1.Department of Algebra and Analysis, Institute of Mathematics and Information Technologies,Uzbekistan Academy of Sciences,Tashkent,Uzbekistan;2.The Abdus Salam International Centre for Theoretical Physics,34151,Italy;3.Department of Mathematics,Karakalpak State University,Nukus,Uzbekistan |
| 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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