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Funktsional'nyi Analiz i ego Prilozheniya, 2007, Volume 41, Issue 4, Pages 70–72
DOI: https://doi.org/10.4213/faa2880 (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
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DOI: https://doi.org/10.4213/faa2880
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.
Received: 21.02.2006
English version:
Functional Analysis and Its Applications, 2007, Volume 41, Issue 4, Pages 303–305
DOI: https://doi.org/10.1007/s10688-007-0028-5
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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