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The Kadec–Pełczyński–Rosenthal subsequence splitting lemma for JBW$^*$-triple preduals

Volume 227 / 2015

Antonio M. Peralta, Hermann Pfitzner Studia Mathematica 227 (2015), 77-95 MSC: Primary 17C65, 46L70, 46B08; Secondary 46B04, 46L51. DOI: 10.4064/sm227-1-5

Abstract

Any bounded sequence in an $L^1$-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec–Pełczyński–Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW$^*$-algebras. In this note we generalize it to JBW$^*$-triple preduals.

Authors

  • Antonio M. PeraltaDepartamento de Análisis Matemático
    Universidad de Granada
    Facultad de Ciencias
    18071 Granada, Spain
    Current address:
    Department of Mathematics
    College of Science
    King Saud University
    P.O. Box 2455-5
    Riyadh 11451, Kingdom of Saudi Arabia
    e-mail
  • Hermann PfitznerUniversité d'Orléans
    BP 6759
    F-45067 Orléans Cedex 2, France
    e-mail

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