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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Our research was supported in part by the grant GAČR P201/12/0290.
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Bohata, M., Hamhalter, J. & Kalenda, O.F.K. On Markushevich bases in preduals of von Neumann algebras. Isr. J. Math. 214, 867–884 (2016). https://doi.org/10.1007/s11856-016-1365-y
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DOI: https://doi.org/10.1007/s11856-016-1365-y