Weakly almost periodic functions and fourier-stieltjes algebras of locally compact groups

A noncompact locally compact group G is called an Eberlein group if W(G) = B(G)^-where W(G) is the algebra of continuous weakly almost periodic functions on G and B(G)^-is the uniform closure of the Fourier-Stieltjes algebra of G. We show that if G is a noncompact [IN]-group or a noncompact nilpotent group then W(G)/B(G)^-contains a linear isometric copy of l^¥In particular, G is not an Eberlein group. On the other hand, finite direct products of Euclidean motion groups and, by a result of W. Veech, noncompact semisimple analytic groups with finite centers are Eberlein groups.