Positivity

, Volume 15, Issue 4, pp 571–594

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

Open AccessArticle

DOI: 10.1007/s11117-011-0127-7

Cite this article as:
Dodds, P.G. & de Pagter, B. Positivity (2011) 15: 571. doi:10.1007/s11117-011-0127-7

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 operatorsProperty (u)Property (V*)

Mathematics Subject Classification (2000)

Primary 46L52Secondary 46E3047A30
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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