Let be an infinite matrix of complex numbers, and be subsets of . Let denote the class of all matrices such that for all and for all , where is the dual of and .
I. J. Maddox in [J. Lond. Math. Soc. 43, 285–290 (1968; Zbl 0155.38802)] introduced and studied the following sets of sequences that are strongly summable and bounded with index () by the Cesàro method of order 1:
In the paper under review, the authors use the characterizations given in [F. Başar, E. Malkowsky and B. Altay, Publ. Math. 73, No. 1–2, 193–213 (2008; Zbl 1164.46003)] of the classes , , , , and and the Hausdorff measure of noncompactness to characterize the classes of compact operators from , and into and .