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An introduction into the theory of sequence spaces and measures of noncompactness. (English) Zbl 0996.46006
Stanković, Bogoljub (ed.), Four topics in mathematics. Beograd: Matematički Institut SANU, Zb. Rad., Beogr. 9(17), 145-234 (2000).

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”.

MSC:
46A45Sequence spaces
47H09Mappings defined by “shrinking” properties
47B07Operators defined by compactness properties
40H05Functional analytic methods in summability
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)