Extendibility of polynomials and analytic functions on $\ell _{p}$
Studia Mathematica, Tome 145 (2001) no. 1, pp. 63-73
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
prove extendible homogeneous polynomials spaces cotype integral allows examples approximable non extendible polynomials ell leq infty degree exhibit non nuclear extendible polynomials infty study extendibility analytic functions banach spaces existence functions infinite radius convergence whose coefficients finite type polynomials which fail extendible
Affiliations des auteurs :
Daniel Carando 1
@article{10_4064_sm145_1_4,
author = {Daniel Carando},
title = {Extendibility of polynomials and analytic functions on $\ell _{p}$},
journal = {Studia Mathematica},
pages = {63--73},
year = {2001},
volume = {145},
number = {1},
doi = {10.4064/sm145-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm145-1-4/}
}
Daniel Carando. Extendibility of polynomials and analytic functions on $\ell _{p}$. Studia Mathematica, Tome 145 (2001) no. 1, pp. 63-73. doi: 10.4064/sm145-1-4
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