(E,F)-Schur multipliers and applications

Fedor Sukochev, and Anna Tomskova. "(E,F)-Schur multipliers and applications." Studia Mathematica 216.2 (2013): 111-129. <http://eudml.org/doc/285870>.

@article{FedorSukochev2013,
abstract = {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 $E = l_\{p\}$, $F = l_\{q\}$). 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 $E = l_\{p\}$, $F = l_\{q\}$.},
author = {Fedor Sukochev, Anna Tomskova},
journal = {Studia Mathematica},
keywords = {Schur multipliers; main triangle projection},
language = {eng},
number = {2},
pages = {111-129},
title = {(E,F)-Schur multipliers and applications},
url = {http://eudml.org/doc/285870},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Fedor Sukochev
AU - Anna Tomskova
TI - (E,F)-Schur multipliers and applications
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 2
SP - 111
EP - 129
AB - 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 $E = l_{p}$, $F = l_{q}$). 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 $E = l_{p}$, $F = l_{q}$.
LA - eng
KW - Schur multipliers; main triangle projection
UR - http://eudml.org/doc/285870
ER -