RT Journal Article
T1 Estimates by polynomials
A1 Llavona, José G.
A1 Aron, R. M.
A1 Choi, Y.S.
AB Consider 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.
PB Cambridge University Press
SN 0004-9727
YR 1995
FD 1995-12
LK https://hdl.handle.net/20.500.14352/57518
UL https://hdl.handle.net/20.500.14352/57518
LA eng
NO NSF
NO KOSEF
NO GARC-KOSEF
NO DGICYT
DS Docta Complutense
RD 10 may 2025