Sufficient Conditions for Factorable Matrices To Be Bounded Operators on Ak

Abstract

A factorable matrix A is a lower triangular matrix with entries a(nk) = a(n)b(k). The sequence space A(k) is defined in (2). In this paper we determine sufficient conditions for a nonnegative factorable matrix A to be a bounded operator on A(k), i.e., A is an element of B(A(k)). As corollaries we obtain sufficient conditions for the discrete Cesdro, terraced, and P-Cesaro matrices defined by Rhaly, to be in B(A(k)).