Absolutely Summing Terraced Matrices

Abstract

Let ∝>0. By C_∝ we mean the terraced matrix defined by c_(nk= 1/n^p ) 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 l^p, to be p- summing , is ∝>1;1≤p<∞. When the more general terraced matrix B, defined by b_nk= β_n if 1≤k≤n and 0 if k>n, is considered, the necessary and sufficient condition turns out to be ∑_n▒〖n^(q/p^* ) 〖|β_n |〗^q<∞〗 in the region 1/p+1/q=1.