González LLavona, José Luis 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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Official URL: http://www.ams.org/journals/proc/1997-125-05/S0002-9939-97-03733-7/S0002-9939-97-03733-7.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 11:13 |
| Last Modified: | 10 Sep 2012 11:13 |
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