Absolutely Summing Terraced Matrices

• Autorzy: Ibrahim Almasri
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Operator; absolutely summing operators; Terraced Matrices

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 1-7

Daty

otrzymano

2015-06-26

zaakceptowano

2015-12-14

online

2016-02-10

Twórcy

autor

Ibrahim Almasri

• Palestine Polytechnic University, Wadi Alharia, P.O.Box 198 Hebron, Palestine

Bibliografia

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

Identyfikatory

DOI

10.1515/conop-2016-0001