Absolutely Summing Terraced Matrices

Abstract

Abstract Let α > 0. By Cα we mean the terraced matrix defined by if 1 ≤ k ≤ n and 0 if k > n. In this paper, we show that a necessary and sufficient condition for the induced operator on lp, to be p-summing, is α > 1; 1 ≤ p < ∞. When the more general terraced matrix B, defined by bnk = βn if 1 ≤ k ≤ n and 0 if k > n, is considered, the necessary and sufficient condition turns out to be in the region 1/p + 1/q ≤ 1.