Llavona, José G.Aron, R. M.Choi, Y.S.2023-06-202023-06-201995-120004-972710.1017/S0004972700014957https://hdl.handle.net/20.500.14352/57518Consider the following possible properties which a Banach space X may have: (P): If (x(j)) and (y(j)) are are bounded sequences in X such that for all n greater than or equal to 1 and for every continuous n-homogeneous polynomial P on X, P(x(j)) - P(y(j)) --> 0, then, Q(x(j) - y(j)) --> 0 for all m greater than or equal to 1 and for every continuous us m-homogeneous polynomial Q on X. (RP): If (x(j)) and (y(j)) are bounded sequences in X such that for all n greater than or equal to 1 and for every continuous n-homogeneous polynomial P on X, P(x(j) - y(j)) --> 0, then Q(x(j)) - Q(y(j)) --> 0 for all m greater than or equal to 1 and for every continuous m-homogeneous polynomial Q on X. We study properties (P) and (RP) and their relation with the Schur property, Dunford-Pettis property, Lambda, and others. Several. applications of these properties are given.engjournal articlehttp://journals.cambridge.org/download.php?file=%2F42139_000CFF88FC69EEF276645126CD9AB357_journals__BAZ_BAZ52_03_S0004972700014957a.pdf&cover=Y&code=4e144b89cb719e9cdb323feb4fadd1e3http://journals.cambridge.org/action/loginrestricted access517.5SpaceAnálisis funcional y teoría de operadores