Llavona, José G.Joaquín M., GutiérrezGonzález, Manuel2023-06-202023-06-2019970002-993910.1090/S0002-9939-97-03733-7https://hdl.handle.net/20.500.14352/57503A 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.engjournal articlehttp://www.ams.org/journals/proc/1997-125-05/S0002-9939-97-03733-7/S0002-9939-97-03733-7.pdfhttp://www.ams.org/journalsopen access517.5Polynomials on Banach spacesWeak polynomial topologyPolynomials on l(1)Análisis funcional y teoría de operadores