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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 4, Pages 70–72 (Mi faa2880)  

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

Derivations of Noncommutative Arens Algebras

Sh. A. Ayupov, K. K. Kudaibergenov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: The present paper deals with derivations of noncommutative Arens algebras. We prove that every derivation of an Arens algebra associated with a von Neumann algebra and a faithful normal finite trace is inner. In particular, each derivation on such algebras is automatically continuous in the natural topology, and in the commutative case, even for semi-finite traces, all derivations are identically zero. At the same time, the existence of noninner derivations is proved for noncommutative Arens algebras with a semi-finite but nonfinite trace.

Keywords: von Neumann algebra, finite trace, Arens algebra, derivation, inner derivation

DOI: https://doi.org/10.4213/faa2880

Full text: PDF file (118 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:4, 303–305

Bibliographic databases:

UDC: 517.98
Received: 21.02.2006

Citation: Sh. A. Ayupov, K. K. Kudaibergenov, “Derivations of Noncommutative Arens Algebras”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 70–72; Funct. Anal. Appl., 41:4 (2007), 303–305

Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ayupov Sh.A., Kudaybergenov K.K., “Derivations on algebras of measurable operators”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 13:2 (2010), 305–337  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ayupov Sh., Kudaybergenov K., “Spatiality of Derivations on the Algebra of Tau-Compact Operators”, Integr. Equ. Oper. Theory, 77:4 (2013), 581–598  crossref  mathscinet  zmath  isi  scopus
    3. Ayupov Sh., Kudaybergenov K., Nurjanov B., Alauadinov A., “Local and 2-Local Derivations on Noncommutative Arens Algebras”, Math. Slovaca, 64:2 (2014), 423–432  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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