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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.

First Page

153

Last Page

166

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Mathematics Commons

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