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2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.
A new measure of noncompactness on Banach spaces is defined from the Hausdorff measure of noncompactness, giving a quantitative version of a classical result by R. S. Phillips. From the main result, classical results are obtained now as corollaries and we have an application to interpolation theory of Banach spaces.
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