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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The non-commutative Yosida-Hewitt decomposition revisited


Authors: P. G. Dodds and B. de Pagter
Journal: Trans. Amer. Math. Soc. 364 (2012), 6425-6457
MSC (2010): Primary 46L52, 46L51; Secondary 46E30
Published electronically: June 26, 2012
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Abstract: In this paper, a new approach to the non-commutative Yosida-Hewitt decomposition is presented in the general setting of non-commutative symmetric spaces of $ \tau $-measurable operators affiliated with semi-finite von Neumann algebras. The principal theorem permits the systematic study of the spaces of normal and singular functionals in this general setting. These results are used to study the properties of elements of order continuous norm and of absolutely continuous norm.


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Additional Information

P. G. Dodds
Affiliation: School of Computer Science, Engineering and Mathematics, Flinders University, GPO Box 2100, Adelaide 5001, Australia
Email: peter@csem.flinders.edu.au

B. de Pagter
Affiliation: Delft Institute of Applied Mathematics, Faculty EEMCS, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
Email: b.depagter@tudelft.nl

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05569-3
PII: S 0002-9947(2012)05569-3
Received by editor(s): May 3, 2010
Received by editor(s) in revised form: February 14, 2011
Published electronically: June 26, 2012
Article copyright: © Copyright 2012 American Mathematical Society