Polynomial continuity on l(1)



Downloads per month over past year

Llavona, José G. and Joaquín M., Gutiérrez and González, Manuel (1997) Polynomial continuity on l(1). Proceedings of the American Mathematical Society, 125 (5). pp. 1349-1353. ISSN 0002-9939

[thumbnail of GLlavona15.pdf]

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


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
Deposited On:10 Sep 2012 09:13
Last Modified:16 Sep 2015 08:12

Origin of downloads

Repository Staff Only: item control page