ar X iv : m at h / 04 07 22 0 v 1 [ m at h . O A ] 1 3 Ju l 2 00 4 DUALITY AND OPERATOR ALGEBRAS
نویسندگان
چکیده
We investigate some subtle and interesting phenomena in the du-ality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are always w *-continuous on dual operator spaces. For example, this yields a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and it makes possible a generalization of the theory of W *-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra.
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