In this paper we shall prove the
following theorem.
Theorem. Suppose 1 < p ≦∞, and rp > 1 if p < ∞, r > 0 if p = ∞. Suppose thematrix A = (ank) with ank= n−r(k ≦ n), ank= 0(k > n). Supposewbe the subsetof w consisting of nonnegative, monotone sequences. Then {nr−1}nis maximum,with respect to <, in I where
I ={b ∈w:for some K > 0,∥A|bx|∥p≦ K∥x∥pfor all x ∈ lp}.