Facebook Instagram Twitter RSS Feed PodBean Back to top on side

On absolute summability for double triangle matrices

In: Mathematica Slovaca, vol. 60, no. 4
Ekrem Savaş - Hamdullah Şevli

Details:

Year, pages: 2010, 495 - 506
Keywords:
bounded operator, double sequence space, triangular matrices, $\mathcal{A}_{k}$ spaces, weighted mean methods
About article:
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 double triangle $T$ to be a bounded operator on $\mathcal{A}k2$; i.e., $T\in B({\mathcal{A}k2})$ for the sequence space $\mathcal{A}k2$ defined below. As special summability methods $T$ we consider weighted mean and double Cesàro, $(C,1,1)$, methods. As a corollary we obtain necessary and sufficient conditions for a double triangle $T$ to be a bounded operator on the space $\mathcal{BV}$ of double sequences of bounded variation.
How to cite:
ISO 690:
Savaş, E., Şevli, H. 2010. On absolute summability for double triangle matrices. In Mathematica Slovaca, vol. 60, no.4, pp. 495-506. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0028-4

APA:
Savaş, E., Şevli, H. (2010). On absolute summability for double triangle matrices. Mathematica Slovaca, 60(4), 495-506. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0028-4
About edition: