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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access February 10, 2016

Absolutely Summing Terraced Matrices

Ibrahim Almasri
From the journal Concrete Operators

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.

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Received: 2015-6-26
Accepted: 2015-12-14
Published Online: 2016-2-10

© 2016 Ibrahim Almasri

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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