Extendibility of polynomials and analytic functions on $\ell _{p}$
Volume 145 / 2001
Studia Mathematica 145 (2001), 63-73
MSC: 46G20, 46G25.
DOI: 10.4064/sm145-1-4
Abstract
We prove that extendible 2-homogeneous polynomials on spaces with cotype 2 are integral. This allows us to find examples of approximable non-extendible polynomials on $\ell _{p}$ $(1\leq p<\infty )$ of any degree. We also exhibit non-nuclear extendible polynomials for $4< p< \infty $. We study the extendibility of analytic functions on Banach spaces and show the existence of functions of infinite radius of convergence whose coefficients are finite type polynomials but which fail to be extendible.
