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Positivity

, Volume 9, Issue 3, pp 457–484 | Cite as

A Non-commutative Yosida–Hewitt Theorem and Convex Sets of Measurable Operators Closed Locally in Measure

  • P. G. Dodds
  • T. K. Dodds
  • F. A. Sukochev
  • O. Ye. Tikhonov
Article

Abstract

We present a non-commutative extension of the classical Yosida–Hewitt decomposition of a finitely additive measure into its σ-additive and singular parts. Several applications are given to the characterisation of bounded convex sets in Banach spaces of measurable operators which are closed locally in measure.

Keywords

non-commutative Banach function spaces singular functionals measurable operators local convergence in measure Köthe duality 

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Copyright information

© Springer 2005

Authors and Affiliations

  • P. G. Dodds
    • 1
  • T. K. Dodds
    • 1
  • F. A. Sukochev
    • 1
  • O. Ye. Tikhonov
    • 2
  1. 1.School of Informatics and EngineeringThe Flinders University of South AustraliaAdelaideAustralia
  2. 2.Research Institute of Mathematics and MechanicsKazan State UniversityKazanRussia

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