Under some assumptions on the pair (A0, B0), we study equivalence betw
een interpolation properties of linear operators and monotonicity cond
itions for a pair (Y, Z) of rearrangement invariant quasi-Banach space
s when the extreme spaces of the interpolation are L(infinity). Weak a
nd restricted weak intermediate spaces fall within our context. Applic
ations to classical Lorentz and Lorentz-Orlicz spaces are given.