Extendibility of polynomials and analytic functions on ${\ell }_p$

Daniel Carando. "Extendibility of polynomials and analytic functions on $ℓ_{p}$." Studia Mathematica 145.1 (2001): 63-73. <http://eudml.org/doc/285370>.

@article{DanielCarando2001,
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 $ℓ_\{p\}$ (1 ≤ p < ∞ ) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. 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.},
author = {Daniel Carando},
journal = {Studia Mathematica},
keywords = {extendible polynomials; integral polynomials; Banach space with cotype 2; non-extendable approximable homogeneous polynomials; extendible holomorphic functions; Taylor expansion},
language = {eng},
number = {1},
pages = {63-73},
title = {Extendibility of polynomials and analytic functions on $ℓ_\{p\}$},
url = {http://eudml.org/doc/285370},
volume = {145},
year = {2001},
}

TY - JOUR
AU - Daniel Carando
TI - Extendibility of polynomials and analytic functions on $ℓ_{p}$
JO - Studia Mathematica
PY - 2001
VL - 145
IS - 1
SP - 63
EP - 73
AB - 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 $ℓ_{p}$ (1 ≤ p < ∞ ) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. 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.
LA - eng
KW - extendible polynomials; integral polynomials; Banach space with cotype 2; non-extendable approximable homogeneous polynomials; extendible holomorphic functions; Taylor expansion
UR - http://eudml.org/doc/285370
ER -