The spaces and of non-absolute type were introduced by the same authors in Part I [Filomat 25, No. 2, 33–51 (2011; Zbl 1265.46011)] as the spaces of all sequences whose -transforms are in the spaces and , respectively, where . The present paper is a natural continuation of the work done in that paper.
The paper is divided mainly in two parts in connection with new results besides the introduction, a general description of the spaces and , and references. In the first part, the -, -, -duals of the spaces and are computed. In the second part, the matrix classes , , , , and , where , are characterized. Further, the authors deduce a characterization of some other classes by means of a given basic lemma.