English

Doob's inequality for non-commutative martingales

Operator Algebras 2007-05-23 v1

Abstract

Let 1p<\81\le p<\8 and (xn)\nen(x_n)_{\nen} be a sequence of positive elements in a non-commutative LpL_p space and (En)\nen(E_n)_{\nen} be an increasing sequence of conditional expectations, then the LpL_p norm of \sum_n E_n(x_n) can be estimated by c_p times the LpL_p 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 1<p\81<p\le \8.

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}
}
R2 v1 2026-07-22T16:45:54.222Z