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Triangles Which are Bounded Operators on A_k

Savas, E., and Sevli, H., and Rhoedes, B.E., (2009) Triangles Which are Bounded Operators on A_k. Bulletin of the Malaysian Mathematical Sciences Society, 32 (2). pp. 223-231. ISSN 0126-6705

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Official URL: http://math.usm.my/bulletin/pdf/v32n2/v32n2p10.pdf

Affiliations

University Uskudar, Turkey. Dept. of Mathematics
Yüzüncü Yıl University, Turkey
Indiana University, USA

Abstract

A lower triangular infinite matrix is called a triangle if there are no zeros on the principal diagonal. The main result of this paper gives a minimal set of sufficient conditions for a triangle $T : \mathcal{A}_{k} \rightarrow\mathcal{A}_{k}$ for the sequence space $\mathcal{A}_{k}$ defined as follows:

$\mathcal{A}_{k} := \{ \{s_n \} : \sum^\infty_{n=1} n^{k-1} \vert a_n \vert^k < \infty , a_n = s_n - s_{n-1} \}.$

2000 Mathematics Subject Classification: 40C05.

Item Type:Journal
Keywords:Bounded operator, triangular matrices, A_k spaces, weighted mean methods.
Subjects:Q Science, Computer Science
ID Code:7780

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[4] B. E. Rhoades, Inclusion theorems for absolute matrix summability methods, J. Math. Anal. Appl. 238 (1999), no. 1, 82–90.

[5] B. E. Rhoades and E. Savas, General inclusion theorems for absolute summability of order k ≥ 1, Math. Inequal. Appl. 8 (2005), no. 3, 505–520.

[6] E. Savas and H. Sevli, On extension of a result of Flett for Cesaro matrices, Appl. Math. Lett. 20 (2007), no. 4, 476–478.

[7] M. Stieglitz and H. Tietz, Matrixtransformationen von Folgenraumen. Eine Ergebnisubersicht, Math. Z. 154 (1977), no. 1, 1–16.

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