1 9 Ja n 20 04 Full extensions and approximate unitary equivalences ∗
نویسنده
چکیده
Let A be a unital separable amenable C∗-algebra and C be a unital C∗-algebra with certain infinite property. We show that two full monomorphisms h1, h2 : A → C are approximately unitarily equivalent if and only if [h1] = [h2] in KL(A,C). Let B be a non-unital but σ-unital C ∗-algebra for which M(B)/B has the certain infinite property. We prove that two full essential extensions are approximately unitarily equivalent if and only if they induce the same element in KL(A,M(B)/B). The set of approximately unitarily equivalence classes of full essential extensions forms a group. If A satisfies the Universal Coefficient Theorem, it is can be identified with KL(A,M(B)/B).
منابع مشابه
∗ - algebras ∗
Let A be a unital separable C∗-algebra and B = C ⊗ K, where C is a unital C∗-algebra. Let τ : A → M(B)/B be a weakly unital full essential extensions of A by B. We show that there is a bijection between a quotient group of K0(B) onto the set of strong unitary equivalence classes of weakly unital full essential extensions σ such that [σ] = [τ ] in KK(A,B). Consequently, when this group is zero, ...
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