m at h . O A ] 2 0 A ug 2 00 4 DUALITY AND OPERATOR ALGEBRAS II : OPERATOR ALGEBRAS AS
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چکیده
We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator spaces, as opposed to that of Banach spaces and Banach algebras. We also answer a natural question about automatic w*-continuity arising in the preceding paper of the authors.
منابع مشابه
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
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) ...
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