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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Dixmier approximation theorem in algebras of measurable operators


Authors: Guy H. Flint, Ben de Pagter and Fedor A. Sukochev
Journal: Proc. Amer. Math. Soc. 141 (2013), 909-918
MSC (2010): Primary 46L51, 47B10; Secondary 46L52
Published electronically: July 2, 2012
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Abstract: In this paper we are concerned with proving versions of the classical Dixmier approximation theorem in the setting of algebras of $ \tau $-measurable operators $ S\left ( \mathcal {M},\tau \right ) $ and its $ \mathcal {M}$-bimodules, where $ \mathcal {M}$ is a semi-finite von Neumann algebra equipped with a semi-finite normal faithful trace $ \tau $.


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Additional Information

Guy H. Flint
Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington 2052, NSW, Australia
Email: guy.flint@gmail.com

Ben de Pagter
Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, Fac. EEMCS, Mekelweg 4, 2628CD Delft, The Netherlands
Email: b.depagter@tudelft.nl

Fedor A. Sukochev
Affiliation: School of Mathematics and Statistics, University of New South Wales, Kensington 2052, NSW, Australia
Email: f.sukochev@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11479-0
PII: S 0002-9939(2012)11479-0
Keywords: Dixmier approximation theorem, $𝜏$-measurable operators, bimodules of measurable operators
Received by editor(s): July 14, 2011
Published electronically: July 2, 2012
Additional Notes: The work of the third author was supported by the ARC
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.