Approximate Unitary Equivalence in Simple C∗-algebras of Tracial Rank One
نویسنده
چکیده
Let C be a unital AH-algebra and let A be a unital separable simple C-algebra with tracial rank no more than one. Suppose that φ, ψ : C → A are two unital monomorphisms. With some restriction on C, we show that φ and ψ are approximately unitarily equivalent if and only if [φ] = [ψ] in KL(C,A) τ ◦ φ = τ ◦ ψ for all tracial states of A and φ = ψ, where φ and ψ are homomorphisms from U0(C)/CU(C) → U0(A)/CU(A) induced by φ and ψ, respectively, and where CU(C) and CU(A) are closures of the subgroup generated by commutators of the unitary groups of C and B. A more practical but approximate version of the above is also presented.
منابع مشابه
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