Projectional Skeletons of Fourier Algebras

Abstract

The preduals of $W^{\ast }$-algebras are 1-Plichko spaces. A natural question arises: does every predual possess a projectional skeleton (PS) $\{P_s:s\in J\}$ such that each $P_s^{\ast }$ is a conditional expectation? In this note, we answer this question affirmatively for the preduals of the group von Neumann algebras of locally compact groups.