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Estimates by polynomials

Llavona, José G. and Aron, R. M. and Choi, Y.S. (1995) Estimates by polynomials. Bulletin of the Australian Mathematical Society, 52 (3 ). 475-486 . ISSN 0004-9727

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Space
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16382
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