Infinite Matrices and Cesàro Sequence Spaces of Non-absolute Type

Abstract

In the present paper we essentially deal with to determine the neccessary and sufficient conditions in order for a matrix A=(a_nk) to belong to the classes (X_p:bs), (X_p:fs), (X₁:l_p), (X_p:X₁) and (l_p:X₁), respectively. Furthermore, we give the sufficient conditions on a matrix A=(a_nk) in the class (X_p:l_p) for 1<p<∞ and prove a Steinhaus type theorem concerning the disjointness of the classes (X_p:fs)_r and (bs:fs). Those sequence spaces are described, below.