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Transactions of the American Mathematical Society

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Sets of uniformly absolutely continuous norm in symmetric spaces of measurable operators


Authors: P. G. Dodds, B. de Pagter and F. Sukochev
Journal: Trans. Amer. Math. Soc. 368 (2016), 4315-4355
MSC (2010): Primary 46L52; Secondary 46E30, 47A30
DOI: https://doi.org/10.1090/tran/6477
Published electronically: September 15, 2015
MathSciNet review: 3453373
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Abstract: We characterise sets of uniformly absolutely continuous norm in strongly symmetric spaces of $ \tau $-measurable operators. Applications are given to the study of relatively weakly compact and relatively compact sets and to compactness properties of operators dominated in the sense of complete positivity by compact or by Dunford-Pettis operators.


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Additional Information

P. G. Dodds
Affiliation: School of Computer Science, Mathematics and Engineering, 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

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

DOI: https://doi.org/10.1090/tran/6477
Keywords: Measurable operators, uniformly absolutely continuous norm, strongly symmetric spaces
Received by editor(s): July 25, 2013
Received by editor(s) in revised form: April 29, 2014
Published electronically: September 15, 2015
Additional Notes: This work was partially supported by the Australian Research Council.
Article copyright: © Copyright 2015 American Mathematical Society

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