Schur and operator multipliers

Ivan G. Todorov, and Lyudmila Turowska. "Schur and operator multipliers." Banach Center Publications 91.1 (2010): 385-410. <http://eudml.org/doc/281814>.

@article{IvanG2010,
abstract = {The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case is presented. Finally, multidimensional versions of Schur and operator multipliers are considered. The article contains a brief discussion of some applications of Schur multipliers, including double operator integrals and multipliers of group algebras.},
author = {Ivan G. Todorov, Lyudmila Turowska},
journal = {Banach Center Publications},
keywords = {Schur product; Schur multiplier; operator multiplier},
language = {eng},
number = {1},
pages = {385-410},
title = {Schur and operator multipliers},
url = {http://eudml.org/doc/281814},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Ivan G. Todorov
AU - Lyudmila Turowska
TI - Schur and operator multipliers
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 385
EP - 410
AB - The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case is presented. Finally, multidimensional versions of Schur and operator multipliers are considered. The article contains a brief discussion of some applications of Schur multipliers, including double operator integrals and multipliers of group algebras.
LA - eng
KW - Schur product; Schur multiplier; operator multiplier
UR - http://eudml.org/doc/281814
ER -