This is an announcement for the paper "(E,F)-multipliers and applications" by Fedor Sukochev and Anna Tomskova.

Abstract: 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 $E=l_p$, $F=l_q$.

Archive classification: math.FA

Remarks: 16 pages

Submitted from: tomskovaanna@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.2623

or

http://arXiv.org/abs/1204.2623