(E,F)-Schur multipliers and applications

• Autorzy: Fedor Sukochev , Anna Tomskova
• Języki publikacji: EN

Abstrakty

EN

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 ∗ 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 $E = l_{p}$, $F = l_{q}$.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 216
• Numer: 2
• Strony: 111-129

Daty

wydano

2013

Twórcy

autor

Fedor Sukochev

• School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

autor

Anna Tomskova

• Institute of Mathematics, National University of Uzbekistan, Tashkent, Durmon yuli 29, 100125, Uzbekistan

Identyfikatory

DOI

10.4064/sm216-2-2