Abstract of a paper by Martin Bohata, Jan Hamhalter and Ondrej F.K. Kalenda
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 or http://arXiv.org/abs/1504.06981
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