Real interpolation for divisible cones

We give necessary and sufficient conditions on a general cone of positive f unctions to satisfy the Decomposition Property (DP) introduced in [5] and c onnect the results with the theory of interpolation of cones introduced by Sagher [9]. One of our main result states that if Q satisfies DP or equival ently is divisible, then for the quasi-normed spaces E-0 and E-1, (Q boolean AND E-0, Q boolean AND E-1)(theta,q) = Q boolean AND (E-0(Q), E- 1(Q))(theta,q), where E-Q = {f; <(Q)over bar f>Q is an element of E} with <(Q)over bar f> = inf {g is an element of Q; \f\ less than or equal to g}. According to this formula, it yields that the interpolation theory for divi sible cones can be easily obtained from the classical theory. 1991 Mathemat ics subject classification: 46M35.