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- W2897280768 abstract "We define a notion of smooth cohomology for $ C^* $-algebras which admit a faithful trace. We show that if $ Asubseteq B(h) $ is a $ C^* $-algebra with a faithful normal trace $ tau $ on the ultra-weak closure $ bar{A} $ of $ mathcal{A} $, and $ X $ is a normal dual operatorial $ bar{A}$-bimodule, then the first smooth cohomology $ mathcal{H}^1_{s}(mathcal{A},X) $ of $ mathcal{A} $ is equal to $ mathcal{H}^1(mathcal{A},X_{tau})$, where $ X_{tau} $ is a closed submodule of $ X $ consisting of smooth elements." @default.
- W2897280768 created "2018-10-26" @default.
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- W2897280768 date "2018-10-18" @default.
- W2897280768 modified "2023-09-27" @default.
- W2897280768 title "Smooth cohomology of $ C^* $-algebras" @default.
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