PROJECTIVE OPERATOR SPACES, ALMOST PERIODICITY AND COMPLETELY COMPLEMENTED IDEALS IN THE FOURIER ALGEBRA

We will show how projective operator spaces arise naturally as spaces of almost periodic functions. In particular, we will show that a locally compact group is compact if and only if its Fourier-Stieltjes algebra (or equivalently its Fourier algebra) is projective as an operator space. From this we see that if K is a compact subgroup of G, then the ideal I(K) is completely complemented in A(G).