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oai:docta.ucm.es:20.500.14352/575032023-07-13T01:06:36Zcom_20.500.14352_14col_20.500.14352_15

Polynomial continuity on l(1) Llavona, José G. Joaquín M., Gutiérrez González, Manuel 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. 2023-06-20T16:57:15Z 2023-06-20T16:57:15Z 1997 journal article 0002-9939 10.1090/S0002-9939-97-03733-7 https://hdl.handle.net/20.500.14352/57503 http://www.ams.org/journals/proc/1997-125-05/S0002-9939-97-03733-7/S0002-9939-97-03733-7.pdf http://www.ams.org/journals eng PB 94-1052 PB 93-0452 open access American Mathematical Society