Abstract
Let A, B be unital C*-algebras and assume that A is separable and quasidiagonal relative to B. Let ϕ, ψ : A → B be unital *-homomorphisms. If A is nuclear and satisfies the UCT, we prove that ϕ is approximately stably unitarily equivalent to ψ if and only if ϕ* = ψ* : K * (A, ℤ/n) → K *(B, ℤ/n) for all n ≥ 0. We give a new proof of a result of [DE2] which states that if A is separable and quasidiagonal relative to B and if (ϕ, ψ : A → B have the same KK-class, then (ϕ is approximately stably unitarily equivalent to ψ. For nuclear separable C*-algebras A, we give a KK-theoretical description of the closure of zero in Ext(A, B).
The author was partially supported by an NSF grant
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Dadarlat, M. (2000). Approximate Unitary Equivalence and the Topology of Ext (A, B). In: Cuntz, J., Echterhoff, S. (eds) C*-Algebras. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57288-3_3
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DOI: https://doi.org/10.1007/978-3-642-57288-3_3
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