Preduals of group von Neumann algebras of locally compact groups possess projectional skeletons in which each adjoint map is a conditional expectation.
Host,Le theoreme des idempotents dansB(G), Bulletin de la Societe Mathematique de France114(1986), 215–223
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Projectional Skeletons of Fourier Algebras
Preduals of group von Neumann algebras of locally compact groups possess projectional skeletons in which each adjoint map is a conditional expectation.