Preduals of von Neumann algebras

Proofs of two assertions are sketched. 1) If the Banach space of a von Neumann algebra 2l is the third dual of some Banach space, then the space a is isometrically isomorphic to the second dual of some von Neumann aluebra A and the von Neumann algebra A is uniquely determined by its enveloping von Neumann algebra (up to von Neumann algebra isomorphism) and is the unique second predual of 2l. (up to isometric isomorphism of Banach spaces). 2) Ail infinite-dimensional von Neumann algebra cannot have preduals of all orders.