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Positivity

, Volume 15, Issue 4, pp 571–594 | Cite as

Properties (u) and (V*) of Pelczynski in symmetric spaces of τ-measurable operators

  • P. G. DoddsEmail author
  • B. de Pagter
Open Access
Article

Abstract

It is shown that order continuity of the norm and weak sequential completeness in non-commutative strongly symmetric spaces of τ-measurable operators are respectively equivalent to properties (u) and (V *) of Pelczynski. In addition, it is shown that each strongly symmetric space with separable (Banach) bidual is necessarily reflexive. These results are non-commutative analogues of well-known characterisations in the setting of Banach lattices.

Keywords

Measurable operators Property (u) Property (V*) 

Mathematics Subject Classification (2000)

Primary 46L52 Secondary 46E30 47A30 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.School of Computer Science, Mathematics and EngineeringFlinders UniversityAdelaideAustralia
  2. 2.Delft Institute of Applied Mathematics, Faculty EEMCSDelft University of TechnologyDelftThe Netherlands

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