Turkish Journal of Mathematics
DOI
10.3906/mat-2009-54
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.
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
