A. M. Bikchentaev, “Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras”, Mat. Zametki, 75:3 (2004), 342–349; Math. Notes, 75:3 (2004), 315

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Matematicheskie Zametki, 2004, Volume 75, Issue 3, Pages 342–349
DOI: https://doi.org/10.4213/mzm36 (Mi mzm36)

This article is cited in 25 scientific papers (total in 25 papers)

Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras

A. M. Bikchentaev

Kazan State University

Full-text PDF (223 kB) Citations (25)

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DOI: https://doi.org/10.4213/mzm36

Abstract: We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra

${\mathscr M}$ into the

$*$ -algebra of measurable operators

$\widetilde {\mathscr M}$ endowed with the topology of convergence in measure is continuous. Using this fact, we prove that the topology of convergence in measure is a minimal one among all metrizable topologies consistent with the ring structure on

$\widetilde {\mathscr M}$ .

Received: 18.12.2002
Revised: 05.08.2003

English version:
Mathematical Notes, 2004, Volume 75, Issue 3, Pages 315–321
DOI: https://doi.org/10.1023/B:MATN.0000023310.15215.c6

Bibliographic databases:

UDC: 517.986+517.987

Language: Russian

Citation: A. M. Bikchentaev, “Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras”, Mat. Zametki, 75:3 (2004), 342–349; Math. Notes, 75:3 (2004), 315–321

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm36

https://doi.org/10.4213/mzm36

https://www.mathnet.ru/eng/mzm/v75/i3/p342

This publication is cited in the following 25 articles:

A. M. Bikchentaev, “Sled i integriruemye kommutatory izmerimykh operatorov, prisoedinennykh k polukonechnoi algebre fon Neimana”, Sib. matem. zhurn., 65:3 (2024), 455–468
A. M. Bikchentaev, O. E. Tikhonov, “Continuity of Operator Functions in the Topology of Local Convergence in Measure”, Proc. Steklov Inst. Math., 324 (2024), 44–52
A. M. Bikchentaev, “The Trace and Integrable Commutators of the Measurable Operators Affiliated to a Semifinite von Neumann Algebra”, Sib Math J, 65:3 (2024), 522
A. M. Bikchentaev, M. F. Darwish, M. A. Muratov, “Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra. II”, Ann. Funct. Anal., 15:3 (2024)
A. M. Bikchentaev, “The topologies of local convergence in measure on the algebras of measurable operators”, Siberian Math. J., 64:1 (2023), 13–21
Ayupov Sh., Kudaybergenov K., “Ring Isomorphisms of -Subalgebras of Murray-Von Neumann Factors”, Lobachevskii J. Math., 42:12 (2021), 2730–2739
Bekjan T.N., Ospanov M.N., “On Young-Type Inequalities of Measurable Operators”, Linear Multilinear Algebra, 2021
Bikchentaev A.M., “On Tau-Essentially Invertibility of Tau-Measurable Operators”, Int. J. Theor. Phys., 60:2, SI (2021), 567–575
Bikchentaev A.M. Sherstnev A.N., “Studies on Noncommutative Measure Theory in Kazan University (1968-2018)”, Int. J. Theor. Phys., 60:2, SI (2021), 585–596
A. M. Bikchentaev, “Seminorms Associated with Subadditive Weights on $C^*$-Algebras”, Math. Notes, 107:3 (2020), 383–391
Bikchentaev A., “Paranormal Measurable Operators Affiliated With a Semifinite Von Neumann Algebra. II”, Positivity, 24:5 (2020), 1487–1501
A. M. Bikchentaev, “Metrics on projections of the von neumann algebra associated with tracial functionals”, Siberian Math. J., 60:6 (2019), 952–956
A. M. Bikchentaev, “Renormalizations of measurable operator ideal spaces affiliated to semi-finite von Neumann algebra”, Ufa Math. J., 11:3 (2019), 3–10
Bikchentaev A.M., “Paranormal Measurable Operators Affiliated With a Semifinite Von Neumann Algebra”, Lobachevskii J. Math., 39:6 (2018), 731–741
A. M. Bikchentaev, “Two classes of $\tau$-measurable operators affiliated with a von Neumann algebra”, Russian Math. (Iz. VUZ), 61:1 (2017), 76–80
A. M. Bikchentaev, “Convergence of integrable operators affiliated to a finite von Neumann algebra”, Proc. Steklov Inst. Math., 293 (2016), 67–76
A. M. Bikchentaev, “Ideal $F$-norms on $C^*$-algebras”, Russian Math. (Iz. VUZ), 59:5 (2015), 58–63
D. Dauitbek, N. E. Tokmagambetov, K. S. Tulenov, “Commutator inequalities associated with polar decompositions of $\tau$-measurable operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 48–52
A. F. Ber, G. B. Levitina, V. I. Chilin, “Derivations with values in quasi-normed bimodules of locally measurable operators”, Siberian Adv. Math., 25:3 (2015), 169–178
A. M. Bikchentaev, “The Haagerup problem on subadditive weights on $W^*$-algebras. II”, Russian Math. (Iz. VUZ), 57:12 (2013), 66–69

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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