Gonzalo, Raquel; Jaramillo, Jesús Angel Compact polynomials between Banach spaces. (English) Zbl 1016.46503 Extr. Math. 8, No. 1, 42-48 (1993). 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. Cited in 2 Documents MSC: 46G25 (Spaces of) multilinear mappings, polynomials 46G20 Infinite-dimensional holomorphy 46B20 Geometry and structure of normed linear spaces Keywords:compact polynomials; Pitt theorem PDFBibTeX XMLCite \textit{R. Gonzalo} and \textit{J. A. Jaramillo}, Extr. Math. 8, No. 1, 42--48 (1993; Zbl 1016.46503) Full Text: EuDML