Quasi-Cesaro matrix and associated sequence spaces

Authors: HADI ROOPAEI, TAJA YAYING

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

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