∗ - algebras ∗
نویسنده
چکیده
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, unitarily equivalent full essential extensions are strongly unitarily equivalent. When B is a non-unital but σ-unital simple C∗-algebra with continuous scale, we also study the problem when two approximately unitarily equivalent essential extensions are strongly approximately unitarily equivalent. A group is used to compute the strongly approximate unitary equivalence classes in the same approximate unitary equivalent class of essential extensions.
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