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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
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