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

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Sharma, Sonia
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Abstract
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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.
Comment: 17 pages, Revision
Keywords
Mathematics - Operator Algebras, Mathematics - Functional Analysis, 46L07, 46B20, 46H10
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