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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
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