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Compact operators between interpolation spaces. (English) Zbl 1150.46009
Summary: We give necessary and sufficient conditions for compactness of operators acting between real \(\mathcal K\)-interpolation spaces for Banach triples. We also establish an estimate for the measure of non-compactness of an interpolation operator for an arbitrary interpolation method when an approximation hypothesis on the image Banach \(N +1\)-tuple is imposed.
MSC:
46B70 Interpolation between normed linear spaces
46M35 Abstract interpolation of topological vector spaces
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