Cesaro mean convergence of martingale differences in rearrangement invariant spaces View Full Text


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Article Info

DATE

2008-07

AUTHORS

Sergey V. Astashkin, Nigel Kalton, Fyodor A. Sukochev

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 L1 holds. More... »

PAGES

387-406

References to SciGraph publications

  • 1989-04. On the weak Dunford-Pettis property in ARCHIV DER MATHEMATIK
  • 1988-12. Martingale inequalities in rearrangement invariant function spaces in ISRAEL JOURNAL OF MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11117-007-2146-y

    DOI

    http://dx.doi.org/10.1007/s11117-007-2146-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1027489411


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