Topologies on central extensions of von Neumann algebras

• Autorzy: Shavkat Ayupov , Karimbergen Kudaybergenov , Rauaj Djumamuratov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

von Neumann algebras; Central extensions; Local measure topology

Kategorie tematyczne

• 46L40: Automorphisms
• 46L51: Noncommutative measure and integration
• 46L57: Derivations, dissipations and positive semigroups in C * -algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 656-664

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Shavkat Ayupov

autor

Karimbergen Kudaybergenov

• Karakalpak State University

autor

Rauaj Djumamuratov

• Karakalpak State University

Bibliografia

• [1] Albeverio S., Ayupov Sh.A., Kudaybergenov K.K., Derivations on the algebra of measurable operators affiliated with a type I von Neumann algebra, Siberian Adv. Math., 2008, 18(2), 86–94 http://dx.doi.org/10.3103/S1055134408020028
• [2] Albeverio S., Ayupov Sh.A., Kudaybergenov K.K., Structure of derivations on various algebras of measurable operators for type I von Neumann algebras, J. Func. Anal., 2009, 256(9), 2917–2943 http://dx.doi.org/10.1016/j.jfa.2008.11.003
• [3] Albeverio S., Ayupov Sh.A., Kudaybergenov K.K., Djumamuratov R.T., Automorphisms of central extensions of type I von Neumann algebras, Studia Math. (in press), preprint available at http://arxiv.org/abs/1104.4698
• [4] Ayupov Sh.A., Kudaybergenov K.K., Derivations on algebras of measurable operators, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 2010, 13(2), 305–337 http://dx.doi.org/10.1142/S0219025710004085
• [5] Ayupov Sh.A., Kudaybergenov K.K., Additive derivations on algebras of measurable operators, J. Operator Theory (in press), preprint available at http://users.ictp.it/_pub_off/preprints-sources/2009/IC2009059P.pdf
• [6] Muratov M.A., Chilin V.I., Algebras of Measurable and Locally Measurable Operators, Proceedings of Institute of Mathematics, Ukrainian Academy of Sciences, 69, Kiev, 2007 (in Russian)
• [7] Muratov M.A., Chilin V.I., Central extensions of *-algebras of measurable operators, Reports of the National Academy of Sciences of Ukraine, 2009, 7, 24–28 (in Russian)
• [8] Muratov M.A., Chilin V.I., (o)-Topology in *-algebras of locally measurable operators, Ukrainian Math. J., 2009, 61(11), 1798–1808 http://dx.doi.org/10.1007/s11253-010-0313-y
• [9] Sarymsakov T.A., Ayupov Sh.A, Khadzhiev Dzh., Chilin V.I., Ordered Algebras, FAN, Tashkent, 1983 (in Russian)
• [10] Segal I.E., A non-commutative extension of abstract integration, Ann. Math., 1953, 57(3), 401–457 http://dx.doi.org/10.2307/1969729
• [11] Yeadon F.J., Convergence of measurable operators, Proc. Cambridge Philos. Soc., 1973, 74, 257–268 http://dx.doi.org/10.1017/S0305004100048052

Identyfikatory

DOI

10.2478/s11533-011-0136-6