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

Fedor Sukochev¹ ; Anna Tomskova²

¹ School of Mathematics and Statistics University of New South Wales Sydney, NSW 2052, Australia
² Institute of Mathematics National University of Uzbekistan Tashkent, Durmon yuli 29, 100125, Uzbekistan

Studia Mathematica, Tome 216 (2013) no. 2, pp. 111-129

Résumé

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

Détail

DOI : 10.4064/sm216-2-2

Mots-clés : given symmetric sequence spaces study multiplier space space matrices which schur product ast maps boundedly whenever does obtain several results asserting continuous embedding multiplier space classical multiplier space furthermore present many examples symmetric sequence spaces whose projective injective tensor products isomorphic subspace banach space unconditional basis extending classical results kwapie czy ski bennett