Factorization and domination of positive Banach–Saks operators

Volume 189 / 2008

Julio Flores, Pedro Tradacete Studia Mathematica 189 (2008), 91-101 MSC: 46B42, 47B65, 47B07. DOI: 10.4064/sm189-1-7


It is proved that every positive Banach–Saks operator $T:E\rightarrow F$ between Banach lattices $E$ and $F$ factors through a Banach lattice with the Banach–Saks property, provided that $F$ has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds–Fremlin sense, are obtained for the class of Banach–Saks operators.


  • Julio FloresDepartment of Applied Mathematics, Escet
    Universidad Rey Juan Carlos
    28933, Móstoles, Madrid, Spain
  • Pedro TradaceteDepartamento de Análisis Matemático
    Facultad de Ciencias Matemáticas
    Universidad Complutense de Madrid
    28040, Madrid, Spain

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