Martingales on von Neumann algebras
TLDR
In this article, the singular martingales on a von Neumann algebra with respect to a given ascending sequence of Von Neumann subalgebras as functionals on the C ∗ -algebra were studied.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1971-04-01 and is currently open access. It has received 110 citations till now. The article focuses on the topics: Abelian von Neumann algebra & Von Neumann algebra.read more
Citations
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Doob's inequality for non-commutative martingales
TL;DR: In this paper, the authors obtained a version of Doob's maximal inequality for the non-commutative case, which is due to Burkholder, Davis and Gundy.
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Noncommutative maximal ergodic theorems
Marius Junge,Quanhua Xu +1 more
TL;DR: In this article, the authors prove the non-commutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on and the analogue of Stein's maximal inequality for symmetric positive contracts.
Book
Martingales in Banach Spaces
TL;DR: In this article, the authors consider the strong p-variation of martingales in non-commutative LP * and show that it is uniformly convex and super-reflexive.
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Non-Commutative Martingale Transforms
TL;DR: In this article, it was shown that non-commutative martingale transforms are of weak type (1,1) and the optimal order of the unconditional Martingale differences (UMD)-constants of the Schatten class S p when p→∞.
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