ESTIMATES BY POLYNOMIALS
SCIE
SCOPUS
- Title
- ESTIMATES BY POLYNOMIALS
- Authors
- ARON, RM; CHOI, YS; LLAVONA, JG
- Date Issued
- 1995-12
- Publisher
- AUSTRALIAN MATHEMATICS PUBL ASSOC INC
- 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.
- Keywords
- SPACE
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21691
- DOI
- 10.1017/S0004972700014957
- ISSN
- 0004-9727
- Article Type
- Article
- Citation
- BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 52, no. 3, page. 475 - 486, 1995-12
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