ON MATRIX SEQUENCES ON $cs$ AND $bs$

Abstract

We respectively denote the linear spaces of bounded double se- quences and bounded double series by M and BS and denote the usual linear spaces of convergent single series and bounded single series by cs and bs. We determine the necessary and sufficient conditions on the sequence $\mathcal{A} = (\mathcal{A}_p)$ of infinite matrices in the classes $(cs, M)$, $(bs, M)$, $(cs, BS)$ and $(bs, BS)$.