Quasi-Cesàro matrix and associated sequence spaces

Abstract

In the present study, we construct a new matrix which we call quasi-Cesàro matrix and is a generalization of the ordinary Cesàro matrix, and introduce BK -spaces C q k and C q∞ as the domain of the quasi-Cesàro matrix C q in the spaces ℓk and ℓ∞, 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∞. 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.