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On Markushevich bases in preduals of von Neumann algebras

Publikace na Matematicko-fyzikální fakulta |
2016

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

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.