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On interpolation of compact operators for Banach triples. (English) Zbl 1004.46046
Summary: We investigate the behaviour of compact operators under \(\mathcal J\) and \(\mathcal K\) interpolation methods with a parameter function of Banach triples. We begin with the case when one of the triples reduces to a single Banach space; then, using the connection between interpolation functors of different orders, we treat the general case for particular Banach triples.
MSC:
46M35 Abstract interpolation of topological vector spaces
47B07 Linear operators defined by compactness properties
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