We generalize an important class of Banach spaces, the M-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided M-embedded operator spaces are the operator spaces which are one-sided M-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon-Nikodým property and many more, are retained in the non-commutative setting. We also discuss the dual setting of one-sided L-embedded operator spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-2,
author = {Sonia Sharma},
title = {Operator spaces which are one-sided M-ideals in their bidual},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {121-141},
zbl = {1195.46058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-2}
}
Sonia Sharma. Operator spaces which are one-sided M-ideals in their bidual. Studia Mathematica, Tome 196 (2010) pp. 121-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-2-2/