Israel Journal of Mathematics

, Volume 214, Issue 2, pp 867–884 | Cite as

On Markushevich bases in preduals of von Neumann algebras

  • Martin Bohata
  • Jan Hamhalter
  • Ondřej F. K. Kalenda
Article

Abstract

We prove that the predual of any von Neumann algebra is 1-Plichko, i.e., it has a countably 1-norming Markushevich basis. This answers a question of the third author who proved the same for preduals of semifinite von Neumann algebras. As a corollary we obtain an easier proof of a result of U. Haagerup that the predual of any von Neumann algebra enjoys the separable complementation property. We further prove that the selfadjoint part of the predual is 1-Plichko as well.

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Copyright information

© Hebrew University of Jerusalem 2016

Authors and Affiliations

  • Martin Bohata
    • 1
  • Jan Hamhalter
    • 1
  • Ondřej F. K. Kalenda
    • 2
  1. 1.Czech Technical University in PragueFaculty of Electrical Engineering, Department of MathematicsPrague 6Czech Republic
  2. 2.Charles University in PragueFaculty of Mathematics and Physics, Department of Mathematical AnalysisPraha 8Czech Republic

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