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. 13491353. ISSN 00029939

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Official URL: http://www.ams.org/journals/proc/199712505/S0002993997037337/S0002993997037337.pdf
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 
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Deposited On:  10 Sep 2012 09:13 
Last Modified:  16 Sep 2015 08:12 
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