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Zbl 1154.47027
De Malafosse, Bruno; Malkowsky, Eberhard; Rakočević, Vladimir
Measure of noncompactness of operators and matrices on the spaces $c$ and $c_{0}$.
(English)
[J] Int. J. Math. Math. Sci. 2006, No. 1, Article ID 46930, 5 p. (2006). ISSN 0161-1712; ISSN 1687-0425/e

The authors, using the Hausdorff measure of noncompactness, give necessary and sufficient conditions for a linear operator, or a matrix, between the spaces $c$ and $c_0$ to be compact. Some results of {\it L.\,W.\thinspace Cohen} and {\it N.\,Dunford} [Duke Math. J. 3, No.4, 689-701 (1937; Zbl 0018.07101; JFM 63.0352.01)] are recovered.
MSC 2000:
*47B37 Operators on sequence spaces, etc.
46B45 Banach sequence spaces
47B07 Operators defined by compactness properties
47H09 Mappings defined by "shrinking" properties

Keywords: compact operators; Hausdorff measure of noncompactness

Citations: Zbl 0018.07101; JFM 63.0352.01

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