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Interpolation of compact operators on Banach triples. (English) Zbl 1004.46048
Summary: Let $$\overline{A}=(A_0,A_1,A_2)$$ and $$\overline{B}=(B_0,B_1,B_2)$$ be $$LP$$-triples (Lions-Peetre triples) of Banach spaces and let $$T$$ be a linear operator. If $$T\colon A_0\to B_0$$ is compact and $$T\colon A_i\to B_i$$ is bounded ($$i=1$$, $$2$$), then also $$T\colon\overline{A}_{f,p}\to \overline{B}_{f,p}$$ is compact, where $$f$$ belongs to the class $$B_{K}^{2}$$ and $$1\leq p\leq \infty$$.
##### MSC:
 46M35 Abstract interpolation of topological vector spaces 47B07 Linear operators defined by compactness properties 46B70 Interpolation between normed linear spaces