Let be the space of all complex sequences , be an infinite matrix of complex numbers and a subset of . The set
is called the matrix domain of in . Given any sets and in , let denote the class of all matrices such that . Let be a triangle, that is, for and , let be the sequence with for all and . The sets of strongly -summable and bounded sequences
were defined and studied by I. J. Maddox [“On Kuttner’s theorem”, J. Lond. Math. Soc. 43, 285–290 (1968; Zbl 0155.38802)].
In the paper under review, the authors apply the Hausdorff measure of noncompactness to characterize the classes of compact operators given by infinite matrices , where is one of spaces or and is the space of null sequences or the space of convergent sequences. Moreover, they give sufficient conditions for the compactness of operators when is again one of spaces or and the final is the space of bounded sequences.