Turkish Journal of Mathematics
Abstract
In the present study, we construct a new matrix which we call quasi-Cesaro matrix and is a generalization of the ordinary Cesaro matrix, and introduce $BK$-spaces $C^q_k$ and $C^q_{\infty}$ as the domain of the quasi-Cesaro matrix $C^q$ in the spaces $\ell_k$ and $\ell_{\infty},$ respectively. Furthermore, we exhibit some topological properties and inclusion relations related to these newly defined spaces. We determine the basis of the space $C^q_k$ and obtain Köthe duals of the spaces $C^q_k$ and $C^q_{\infty}.$ Based on the newly defined matrix, we present a factorization for the Hilbert matrix and generalize Hardy's inequality, as an application. Moreover we find the norm of this new matrix as an operator on several matrix domains.
DOI
10.3906/mat-2009-54
Keywords
Matrix operator, Hilbert matrix, Cesaro matrix, norm, sequence space
First Page
153
Last Page
166
Recommended Citation
ROOPAEI, HADI and YAYING, TAJA
(2021)
"Quasi-Cesaro matrix and associated sequence spaces,"
Turkish Journal of Mathematics: Vol. 45:
No.
1, Article 10.
https://doi.org/10.3906/mat-2009-54
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss1/10
