Gundy's decomposition for non-commutative martingales and applications

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dc.creatorParcet, Javier
dc.creatorRandrianantoanina, Narcisse
dc.date2004-11-12
dc.date2005-08-26
dc.date.accessioned2026-07-07T05:14:17Z
dc.date.available2026-07-07T05:14:17Z
dc.descriptionWe provide an analogue of Gundy's decomposition for L1-bounded non-commutative martingales. An important difference from the classical case is that for any L1-bounded non-commutative martingale, the decomposition consists of four martingales. This is strongly related with the row/column nature of non-commutative Hardy spaces of martingales. As applications, we obtain simpler proofs of the weak type (1,1) boundedness for non-commutative martingale transforms and the non-commutative analogue of Burkholder's weak type inequality for square functions. A sequence (x_n) in a normed space X is called 2-co-lacunary if there exists a bounded linear map from the closed linear span of (x_n) to l2 taking each x_n to the n-th vector basis of l2. We prove (using our decomposition) that any relatively weakly compact martingale difference sequence in L1(M,τ) whose sequence of norms is bounded away from zero is 2-co-lacunary, generalizing a result of Aldous and Fremlin to non-commutative L1-spaces.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0411296
dc.identifierhttp://arxiv.org/abs/math/0411296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73221
dc.subjectOperator Algebras
dc.subjectProbability
dc.subject46L53, 46L52 (Primary) 46L51, 60G42 (Secondary)
dc.titleGundy's decomposition for non-commutative martingales and applications
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