Unconditional martingale difference sequences in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:326

Article

Cullender, Stuart R. ; Labuschagne, Coenraad C. A.

关键词: Banach space;    Banach lattice;    filtration;    martingale difference sequence;    basis;   

DOI  :  10.1016/j.jmaa.2006.03.061

来源: Elsevier

【 摘 要 】

For a Banach space Y, the question of whether L(p) (mu, Y) has an unconditional basis if 1 < p < infinity and Y has unconditional basis, stood unsolved for a long time and was answered in the negative by Aldous. In this work we prove a weaker, positive result related to this question. We show that if (y(j)) is a basis of Y and (d(i)) is a martingale difference sequence spanning L(p)(mu) then the sequence (d(i) circle times y(j)) is a basis of L(p)(mu, Y) for 1 <= p < infinity. Moreover, if 1 < p < infinity and (y(j)) is unconditional then (d(i) circle times y(j)) is strictly dominated by an unconditional tensor product basis. In addition, for 1 < p < infinity, we show that if (d(i)) subset of L(p)(mu) is a martingale difference sequence then there exists a constant K > 0 so that [GRAPHICS] holds for every sequence (y(j)) subset of Y and every choice of finitely supported scalars (alpha(ij)). (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free