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Measure of non-compactness and Sparr’s interpolation methods. (English) Zbl 1199.46165
Summary: We establish an estimate for the measure $$\beta (T)$$ of non-compactness of an operator $$T$$ acting from some intermediate spaces $$A$$ with respect to Banach $$n$$-tuples $$\overline A$$ into some intermediate space $$B$$ with respect to Banach $$n$$-tuples $$\overline B$$. We begin with the case when one of the $$n$$-tuples is reduced to a single Banach space and, later, we will treat the general case.
##### MSC:
 46M35 Abstract interpolation of topological vector spaces 46B70 Interpolation between normed linear spaces