Biblioteca de la Universidad Complutense de Madrid

Polynomial continuity on l(1)


Llavona, José G. y Joaquín M., Gutiérrez y González, Manuel (1997) 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.

Tipo de documento:Artículo
Palabras clave:Polynomials on Banach spaces; Weak polynomial topology; Polynomials on l(1)
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16256

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

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Última Modificación:16 Sep 2015 08:12

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