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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
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norm one approximate identities in separable C* algebras
I'm trying to prove Corollary 1.4.9 in K. Davidson's book (Exercise 1.5):
If A is a separable C* algebra, then there is an increasing sequence
$E_i, i=1,...,\infty$ of positive norm-one elements whic …