Absolutely Summing Terraced Matrices

Ibrahim Almasri

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 1-7
  • ISSN: 2299-3282

Abstract

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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.

How to cite

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Ibrahim Almasri. "Absolutely Summing Terraced Matrices." Concrete Operators 3.1 (2016): 1-7. <http://eudml.org/doc/276535>.

@article{IbrahimAlmasri2016,
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.},
author = {Ibrahim Almasri},
journal = {Concrete Operators},
keywords = {Operator; absolutely summing operators; Terraced Matrices; terraced matrix},
language = {eng},
number = {1},
pages = {1-7},
title = {Absolutely Summing Terraced Matrices},
url = {http://eudml.org/doc/276535},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Ibrahim Almasri
TI - Absolutely Summing Terraced Matrices
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 1
EP - 7
AB - 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.
LA - eng
KW - Operator; absolutely summing operators; Terraced Matrices; terraced matrix
UR - http://eudml.org/doc/276535
ER -

References

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  1. [1] G. Bennett, Some Elementary Inequalities, Quart. J. Math. Oxford (2), 38 (1987), 401-425.  Zbl0649.26013
  2. [2] G Bennett, Some Ideas of Operators on Hilbert Space, Studia Mathematica, T. LV. (1976), 27-39.  Zbl0338.47013
  3. [3] J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge University Press, 1995.  Zbl0855.47016
  4. [4] J. Fridy, Abel Transformation into l1, Cand. Math. Bull., vol. 25(4), 1982, 421-427.  Zbl0437.40006
  5. [5] G. Jameson, Summing and Nuclear Norms in Banach Space Theory, Cambridge University Press, 1987.  Zbl0634.46007
  6. [6] S. Kwapien, A remark on p-absolutely summing operators in lrspaces, Studia Math., 34 ( 1970), 109-111.  Zbl0189.43601
  7. [7] A Pietsch, Absolute p-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1967), 333-353.  Zbl0156.37903
  8. [8] H. Rhaly, p-Cesaro Matrices, Houston Journal of Mathematics, vol. 15, no. 1, 1989, 137-146.  Zbl0691.47026

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