Complutense University Library

Polynomial continuity on l(1)

Llavona, José G. and Joaquín M., Gutiérrez and González, Manuel Polynomial continuity on l(1). Proceedings of the American Mathematical Society, 125 (5). pp. 1349-1353. ISSN 0002-9939

[img] PDF
Restricted to Repository staff only until 31 December 2020.

186kB

Official URL: http://www.ams.org/journals/proc/1997-125-05/S0002-9939-97-03733-7/S0002-9939-97-03733-7.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space X has property(RP) if given two bounded sequences (u(j)), (v(j)) subset of X; we have that Q(u(j)) - Q(v(j)) --> 0 for every polynomial Q on X whenever P(u(j) - v(j)) --> 0 for every polynomial P on XI i.e., the restriction of every polynomial on X to each bounded set is uniformly sequentially continuous for the weak polynomial topology. We show that property (RP) does not imply that every scalar valued polynomial on X must be polynomially continuous.


Item Type:Article
Uncontrolled Keywords:Polynomials on Banach spaces; Weak polynomial topology; Polynomials on l(1)
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16256
References:

R. M. Aron, Y. S. Choi and J. G. Llavona, Estimates by polynomials, Bull. Austral. Math. Soc. 52 (1995), 475-486. CMP 96:03

R. M. Aron and J. B. Prolla, Polynomial approximation of diferentiable functions on Banach spaces, J. Reine Angew. Math. 313 (1980), 195-216. MR 81c:41078

T. K. Carne, B. Cole and T. W. Gamelin, A uniform algebra of analytic functions on a Banach space, Trans. Amer. Math. Soc. 314 (1989), 639-659. MR 90i:46098

A. M. Davie and T. W. Gamelin, A theorem on polynomial-star approximation, Proc. Amer. Math. Soc. 106 (1989), 351-356. MR 89k:46023

J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, Springer, Berlin 1984. MR 85i:46020

J. Mujica, Complex Analysis in Banach Spaces, Math. Studies 120, North-Holland, Amster- dam 1986. MR 88d:46084

Deposited On:10 Sep 2012 09:13
Last Modified:07 Feb 2014 09:25

Repository Staff Only: item control page