Gonzalo, Raquel; Jaramillo, Jesús Angel Compact polynomials between Banach spaces. (English) Zbl 0853.46039 Proc. R. Ir. Acad., Sect. A 95, No. 2, 213-226 (1995). Summary: For every Banach space \(X\) we introduce indexes \(l(X)\) and \(u(X)\) in connection with the existence of upper and lower \(\ell_p\)-estimates for sequences in \(X\). These indexes are compared with type and cotype of space. We prove that polynomials preserve upper estimates of sequences, and we deduce that every polynomial \(P: X\to Y\) of degree \(N\) is compact when \(N\cdot u(Y)< l(X)\) and \(X\) does not contain a copy of \(\ell_1\). Cited in 8 Documents MSC: 46G20 Infinite-dimensional holomorphy 46B20 Geometry and structure of normed linear spaces Keywords:upper and lower \(\ell_ p\)-estimates; type; cotype; polynomials; degree PDFBibTeX XMLCite \textit{R. Gonzalo} and \textit{J. A. Jaramillo}, Proc. R. Ir. Acad., Sect. A 95, No. 2, 213--226 (1995; Zbl 0853.46039)