Abstract
We study the class of r.i. spaces in which Cesaro means of any weakly null martingale difference sequence is strongly null. This property is related to the Banach-Saks property. We show that in classical (separable) r.i. spaces (such as Orlicz, Lorentz and Marcinkiewicz spaces) these properties coincide but this is no longer true for general r.i. spaces. We locate also a class of r.i. spaces having this property where an analogue of the classical Dunford-Pettis characterization of relatively weakly compact subsets in L 1 holds.
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Research was partially supported by the ARC and NSF grant DMS-0244515.
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Astashkin, S.V., Kalton, N. & Sukochev, F.A. Cesaro mean convergence of martingale differences in rearrangement invariant spaces. Positivity 12, 387–406 (2008). https://doi.org/10.1007/s11117-007-2146-y
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DOI: https://doi.org/10.1007/s11117-007-2146-y