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Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Sep 5, 2014 at 7:39 comment added AlexE I think the answer to my own question here should be no. Note that we have for the commutator $[\Psi^0, \Psi^0] \subset \Psi^{-1}$ and this inclusion passes of course to the completions. Now $\overline{\Psi^{-1}}$ are exactly all the compact operators $\mathfrak{K}$ since $M$ is compact. So the quotient $\overline{\Psi^0} / \mathfrak{K}$ is abelian, whereas $D^\ast(M) / \mathfrak{K}$ should not be abelian.
Apr 12, 2014 at 13:48 history asked AlexE CC BY-SA 3.0