Operator martingale decomposition and the Radon-Nikodym property in Banach spaces

Valeria Marraffa, Coenraad C.A. Labuschagne

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4 Citazioni (Scopus)

Abstract

We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon-Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney-Schaefer l-tensor product E over(⊗, ̃)l Y, where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon-Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E over(⊗, ̃)l Y. Secondly, we derive a Riesz decomposition for uniform amarts of maps acting between a Banach lattice and a Banach space. This result is used to characterize Banach spaces with the Radon-Nikodým property in terms of uniformly norm bounded uniform amarts of maps that are norm convergent. In the case 1 < p < ∞, our results yield Lp (μ, Y)-space analogues of some of the well-known results on uniform amarts in L1 (μ, Y)-spaces
Lingua originaleEnglish
pagine (da-a)357-365
Numero di pagine9
RivistaJournal of Mathematical Analysis and Applications
Volume363
Stato di pubblicazionePublished - 2010

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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