On Markushevich bases in preduals of von Neumann algebras
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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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- N. Ghoussoub, G. Godefroy, B. Maurey and W. Schachermayer, Some topological and geometrical structures in Banach spaces, Memoirs of the American Mathematical Society 70 (1987).Google Scholar
- R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras. Vol. I, Graduate Studies in Mathematics, Vol. 15, American Mathematical Society, Providence, RI, 1997.Google Scholar
- A. N. Plichko, E-mail to the third author, December 1999.Google Scholar
- S. Sakai, C*-Algebras and W*-Algebras, Classics in Mathematics, Springer-Verlag, Berlin–Heidelberg–New York, 1998.Google Scholar