Voiculescu Theorem, Sobolev Lemma, and Extensions of Smooth Algebras
نویسندگان
چکیده
We present the analytic foundation of a unified B-D-F extension functor Extr on the category of noncommutative smooth algebras, for any Fréchet operator ideal ^ . Combining the techniques devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth algebras and Fréchet operator ideals. A key notion involved is r-smoothness, which is verified for the algebras of smooth functions, via a noncommutative Sobolev lemma. The groups Extr are computed for many examples.
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