SOME INEQUALITIES INVOLVING LOWER BOUNDS OF OPERATORS ON WEIGHTED SEQUENCE SPACES BY A MATRIX NORM

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma- trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the following inequality: k Ax kv;B(q) L k x kv;B(p); where x  0 and x 2 lp(v;B) and also v = (vn)1 n=1 is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for Lv;p;q;B(H), where H is the Hausdor matrix and 0 < q  p  1. Also for the case p = 1, we obtain kAkw;B(1), and for the case p  1, we obtain Lw;B(p)(A).