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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-23,
author = {Ivan G. Todorov and Lyudmila Turowska},
title = {Schur and operator multipliers},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {385-410},
zbl = {1223.47116},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-23}
}
Ivan G. Todorov; Lyudmila Turowska. Schur and operator multipliers. Banach Center Publications, Tome 89 (2010) pp. 385-410. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-23/