  Let X be a smooth projective variety of dimension n on which rational and
homological equivalence coincide for algebraic p-cycles in the range 0\leq
p\leq s. We show that the homologically trivial sector of rational Lawson
homology L_pH_k(X,Q)_{hom} vanishes for 0\leq n-p\leq s+2. This is an analogue
of a theorem of C. Peters in "dual dimensions". Together with Peters' theorem
we get that the natural transformation L_pH_k(X,Q)--> H_k(X,Q) is injective for
all p and k when X is a smooth projective variety of dimension 4 and Ch_0(X)
=Z.
