Doob's inequality for non-commutative martingales
Operator Algebras
2007-05-23 v1
Abstract
Let and be a sequence of positive elements in a non-commutative space and be an increasing sequence of conditional expectations, then the norm of \sum_n E_n(x_n) can be estimated by c_p times the norm of \sum_n x_n. This inequality is due to Burkholder, Davis and Gundy in the commutative case. By duality, we obtain a version of Doob's maximal inequality for .
Keywords
Cite
@article{arxiv.math/0206062,
title = {Doob's inequality for non-commutative martingales},
author = {M. Junge},
journal= {arXiv preprint arXiv:math/0206062},
year = {2007}
}