Voiculescu theorem, Sobolev lemma, and extensions of smooth algebras

Xiaolu Wang

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arXiv · math/9210227

Voiculescu theorem, Sobolev lemma, and extensions of smooth algebras

Xiaolu Wang

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Abstract

We present the analytic foundation of a unified B-D-F extension functor $\operatorname{Ext}_\tau$ on the category of noncommutative smooth algebras, for any Fr\'echet operator ideal $\Cal K_\tau$. Combining the techniques devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth algebras and Fr\'echet operator ideals. A key notion involved is $\tau$-smoothness, which is verified for the algebras of smooth functions, via a noncommutative Sobolev lemma. The groups $\operatorname{Ext}_\tau$ are computed for many examples.

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Xiaolu Wang. 1992-10-01. Voiculescu theorem, Sobolev lemma, and extensions of smooth algebras. https://arxiv.org/abs/math/9210227

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