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

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Invertibility modulo the intersection of ideals in $C^*$-algebras

This is a crosspost from math.se because it did not get any attention whatsoever. I therefore assume that it fits here better. Let $\mathcal{A}$ be a $C^*$-algebra and $A \in \mathcal{A}$. I am inter …