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 , ). 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 , .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-2,
author = {Fedor Sukochev and Anna Tomskova},
title = {(E,F)-Schur multipliers and applications},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {111-129},
zbl = {1281.47023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-2}
}
Fedor Sukochev; Anna Tomskova. (E,F)-Schur multipliers and applications. Studia Mathematica, Tome 215 (2013) pp. 111-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-2/