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Eurasian Math. J., 2014, Volume 5, Number 1, Pages 82–94 (Mi emj150)  

This article is cited in 1 scientific paper (total in 1 paper)

On a certain class of operator algebras and their derivations

Sh. A. Ayupovab, R. Z. Abdullaeva, K. K. Kudaybergenovc

a Dormon yoli 29, Institute of Mathematics, National University of Uzbekistan, 100125 Tashkent, Uzbekistan
b Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
c Department of Mathematics, Karakalpak State University, 1 Abdirov St., 142012, Nukus, Uzbekistan

Abstract: Given a von Neumann algebra $M$ with a faithful normal finite trace, we introduce the so-called finite tracial algebra $M_f$ as the intersection of $L_p$-spaces $L_p(M,\mu)$ over all $p\geqslant1$ and over all faithful normal finite traces $\mu$ on $M$. Basic algebraic and topological properties of finite tracial algebras are studied. We prove that all derivations on these algebras are inner.

Keywords and phrases: von Neumann algebra, faithful normal finite trace, non commutative $L_p$-spaces, Arens algebra, finite tracial algebra, derivations.

Full text: PDF file (428 kB)
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MSC: 46L51, 46L52, 46L57, 46L07
Received: 06.04.2011
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Citation: Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov, “On a certain class of operator algebras and their derivations”, Eurasian Math. J., 5:1 (2014), 82–94

Citation in format AMSBIB
\Bibitem{AyuAbdKud14}
\by Sh.~A.~Ayupov, R.~Z.~Abdullaev, K.~K.~Kudaybergenov
\paper On a certain class of operator algebras and their derivations
\jour Eurasian Math. J.
\yr 2014
\vol 5
\issue 1
\pages 82--94
\mathnet{http://mi.mathnet.ru/emj150}


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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. R. Abdullaev, “Tracial and Arens algebras associated with finite von Neumann algebras”, Topics in Functional Analysis and Algebra, Contemporary Mathematics, 672, eds. B. Russo, A. Aksoy, R. Ashurov, S. Ayupov, Amer. Math. Soc., 2016, 1–7  crossref  mathscinet  zmath  isi
  • Eurasian Mathematical Journal
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