arXiv math/04072202004-07-16math.OAmath.FA

Duality and operator algebras

David P. Blecher, Bojan Magajna

备注：: 19 pages (An error corrected, and results slightly reordered)

英文摘要：

We investigate some subtle and interesting phenomena in the duality 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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