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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

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Is the algebra of compact operators flat?

Suppose that $A\hookrightarrow B$ is an inclusion of $C^*$-algebras and let $K$ be the algebra of compact operators on a separable Hilbert space. Is it true that the map $A\otimes K\hookrightarrow B\o …
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