(E,F)-multipliers and applications

Details (E,F)-multipliers and applications (E,F)-multipliers and applications

2012-04-12

arxiv.org/abs/1204.2623v1

Mathematics

Functional Analysis

16 pages

Scientific paper

For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is the space all of 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 $(E,F)$-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. Kwapie\'{n} and A. Pe{\l}czy\'{n}ski and of G. Bennett for the case when $E=l_p$, $F=l_q$.

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