This is an announcement for the paper "On Markushevich bases in preduals of von Neumann algebras" by Martin Bohata, Jan Hamhalter and Ondrej F.K. Kalenda.
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 self-adjoint part of the predual is $1$-Plichko as well.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B26, 46L10
Remarks: 13 pages
Submitted from: kalenda@karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.06981
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