Operator spaces which are one-sided M-Ideals in their bidual

Details Operator spaces which are one-sided M-Ideals in their bidual Operator spaces which are one-sided M-Ideals in their bidual

2009-02-24

arxiv.org/abs/0902.4257v2

Mathematics

Operator Algebras

17 pages, Revision

Scientific paper

We generalize an important class of Banach spaces, namely 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 Nikod$\acute {\rm{y}}$m Property and many more, are retained in the non-commutative setting. We also discuss the dual setting of one-sided $L$-embedded operator spaces.

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