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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.

Abstract. The order topology τ o (P ) (resp. the sequential order topology τ os (P )) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part M sa , the self-adjoint part of the unit ball M 1 sa , and the projection lattice P (M ). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other standard locally convex topologies on M , and relate the properties of the order topology to the underlying operatoralgebraic structure of M .