Absolutely Summing Terraced Matrices

Abstract

Let α > . By Cα we mean the terraced matrix de ned by c nk = n α if ≤ k ≤ n and if k > n. In this paper, we show that a necessary and su cient condition for the induced operator on l p , to be p-summing, is α > ; ≤ p < ∞. When the more general terraced matrix B, de ned by b nk = βn if ≤ k ≤ n and if k > n, is considered, the necessary and su cient condition turns out to be n n q p * | βn | q < ∞ in the region /p + /q ≤ .

The critical point and the $p$-norm of $A_s$ and $C$-matrices

“…The same author then published six more articles on this subject, with his latest being in 2013 [10]. Other examples of studies of the C-matrices include Roades [11], who provide lower bounds of p-norms of these matrices under certain restrictions on p, Almasri [12] show that the C-matrix defined by the sequence 1/n α is p-summing if and only if α > 1, and Durna & Yildirim [13] introduced and studied the generalized terraced matrices.…”