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Concrete Operators

Ed. by Ross, William / Mashreghi, Javad

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Mathematical Citation Quotient (MCQ) 2016: 0.38


Emerging Science

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2299-3282
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Absolutely Summing Terraced Matrices

Ibrahim Almasri
  • Corresponding author
  • Palestine Polytechnic University, Wadi Alharia, P.O.Box 198 Hebron, Palestine
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-02-10 | DOI: https://doi.org/10.1515/conop-2016-0001

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.

Keywords: Operator; absolutely summing operators; Terraced Matrices

References

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  • [5] G. Jameson, Summing and Nuclear Norms in Banach Space Theory, Cambridge University Press, 1987. Google Scholar

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  • [8] H. Rhaly, p-Cesaro Matrices, Houston Journal of Mathematics, vol. 15, no. 1, 1989, 137-146. Google Scholar

About the article

Received: 2015-06-26

Accepted: 2015-12-14

Published Online: 2016-02-10


Citation Information: Concrete Operators, Volume 3, Issue 1, Pages 1–7, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2016-0001.

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© 2016 Ibrahim Almasri. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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