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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 4, Pages 73–78 (Mi faa2881)  

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

Brief communications

The Representation Theorem for Local Operator Spaces

A. A. Dosiev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: In this note we propose a representation theorem for local operator spaces which extends Ruan's representation theorem for operator spaces, and Arveson–Hahn–Banach–Webster theorem for local operator systems. Further, we investigate the decomposition property of a complete contraction from a unital multinormed $C^*$-algebra into a local operator system as a product of contractions and unital contractive $*$-representation, and the injectivity in both local operator space and local operator system contexts.

Keywords: local operator space, local operator system, multinormed $C^*$-algebra

DOI: https://doi.org/10.4213/faa2881

Full text: PDF file (155 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:4, 306–310

Bibliographic databases:

UDC: 517.98
Received: 16.02.2006

Citation: A. A. Dosiev, “The Representation Theorem for Local Operator Spaces”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 73–78; Funct. Anal. Appl., 41:4 (2007), 306–310

Citation in format AMSBIB
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\by A.~A.~Dosiev
\paper The Representation Theorem for Local Operator Spaces
\jour Funktsional. Anal. i Prilozhen.
\yr 2007
\vol 41
\issue 4
\pages 73--78
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\transl
\jour Funct. Anal. Appl.
\yr 2007
\vol 41
\issue 4
\pages 306--310
\crossref{https://doi.org/10.1007/s10688-007-0029-4}
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Linking options:
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  • https://doi.org/10.4213/faa2881
  • http://mi.mathnet.ru/eng/faa/v41/i4/p73

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

    This publication is cited in the following articles:
    1. Dosiev A., “Local operator spaces, unbounded operators and multinormed $C^*$-algebras”, J. Funct. Anal., 255:7 (2008), 1724–1760  crossref  mathscinet  zmath  isi  scopus
    2. Dosi A., “Quantum duality, unbounded operators, and inductive limits”, J. Math. Phys., 51:6 (2010), 063511, 43 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Dosi A., “Injectivity in the Quantum Space Framework”, Oper. Matrices, 8:4 (2014), 1013–1039  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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