l(1)-CONTRACTIVE MAPS ON NONCOMMUTATIVE L-p-SPACES

Let T : L-p (M) -> L-p (N) be a bounded operator between two noncommutative L-p-spaces, 1 <= p < infinity. We say that T is l(1)-bounded (respectively l(1)-contractive) if T circle times I-l1 extends to a bounded (respectively contractive) map from L-p (M; l(1)) into L-p (N; l(1)). We show that Yeadon's factorization theorem for L-p-isometries, 1 <= p not equal 2 < infinity, applies to an isometry T : L-2 (M) -> L-2 (N) if and only if T is l(1)-contractive. We also show that a contractive operator T : L-p (M) -> L-p (N) is automatically l(1)-contractive if it satisfies one of the following two conditions: either T is 2-positive; or T is separating, that is, for any disjoint a, b is an element of L-p (M) (i.e. a*b = ab* = 0), the images T (a), T (b) are disjoint as well.