$(E,F)$-Schur multipliers and applications
Tom 216 / 2013
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 $E=l_p$, $F=l_q$.