Operator spaces which are one-sided $M$-ideals in their bidual

Sonia Sharma ¹

¹ Department of Mathematics University of Houston Houston, TX 77204, U.S.A.

Studia Mathematica, Tome 196 (2010) no. 2, pp. 121-141

Résumé

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.

Détail

DOI : 10.4064/sm196-2-2

Keywords: generalize important class banach spaces m embedded banach spaces non commutative setting operator spaces one sided m embedded operator spaces operator spaces which one sided m ideals their second dual several properties classical setting stability under taking subspaces quotients unique extension property radon nikod property many retained non commutative setting discuss dual setting one sided l embedded operator spaces