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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

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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:07 Feb 2014 09:25

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