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Compact polynomials between Banach spaces. (English) Zbl 1016.46503
Summary: The classical Pitt theorem asserts that every bounded linear operator from $$\ell_p$$ into $$\ell_q$$ is compact whenever $$q< p$$. This result was extended by Pelczynski who showed in particular that every $$N$$-homogeneous polynomial from $$\ell_p$$ into $$\ell_q$$ is compact if $$Nq< p$$. Our aim of this note is giving conditions on Banach spaces $$X$$ and $$Y$$ in order to obtain that every polynomial of a given degree $$N$$ from $$X$$ into $$Y$$ is compact.

##### MSC:
 46G25 (Spaces of) multilinear mappings, polynomials 46G20 Infinite-dimensional holomorphy 46B20 Geometry and structure of normed linear spaces
##### Keywords:
compact polynomials; Pitt theorem
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