$(E,F)$-Schur multipliers and applications

Tom 216 / 2013

Fedor Sukochev, Anna Tomskova Studia Mathematica 216 (2013), 111-129 MSC: Primary 47B49; Secondary 47B37. DOI: 10.4064/sm216-2-2

Streszczenie

For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is, the space of all matrices $M$ for which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever $A$ does. We obtain several results asserting continuous embedding of the $(E,F)$-multiplier space into the classical $(p,q)$-multiplier space (that is, when $E=l_p$, $F=l_q$). Furthermore, we present many examples of symmetric sequence spaces $E$ and $F$ whose projective and injective tensor products are not isomorphic to any subspace of a Banach space with an unconditional basis, extending classical results of S. Kwapień and A. Pełczyński (1970) and of G. Bennett (1976, 1977) for the case when $E=l_p$, $F=l_q$.

Autorzy

  • Fedor SukochevSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, NSW 2052, Australia
    e-mail
  • Anna TomskovaInstitute of Mathematics
    National University of Uzbekistan
    Tashkent, Durmon yuli 29, 100125, Uzbekistan
    e-mail

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