Operator Spaces Which Are One-sided M-ideals in Their Bidual
نویسنده
چکیده
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 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.
منابع مشابه
One - Sided M - Ideals and Multipliers in Operator Spaces , I
The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is...
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