*(English)*Zbl 0996.46006

From the authors’ preface: “This paper gives a self-contained, comprehensive treatment of the theories of sequence spaces and measures of noncompactness, as well as a survey of some of the authors’ recent research results in these fields. For the first time, methods from the fields of summability, in particular of sequence spaces and matrix transformations on one hand, and of measures of noncompactness on the other are successfully linked on a large scale to obtain necessary and sufficient conditions for matrix maps between certain sequence spaces of a general class to be compact operators.

These notes are addressed to both experts and nonexperts with an interest in getting acquainted with sequence spaces and measures of noncompactness. They could also be used as a guideline for research and teaching at graduate and postgraduate levels”.