Full extensions and approximate unitary equivalences

Huaxin Lin

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arXiv · math/0401242

Full extensions and approximate unitary equivalences

Huaxin Lin

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Abstract

Let $A$ be a unital separable amenable \CA and $C$ be a unital \CA with certain infinite property. We show that two full monomorphisms $h_1, h_2: A\to C$ are approximately unitarily equivalent if and only if $[h_1]=[h_2]$ in $KL(A,C).$ Let $B$ be a non-unital but $σ$-unital \CA 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 $KL(A, M(B)/B).$

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BibTeX RIS

Huaxin Lin. 2004-01-19. Full extensions and approximate unitary equivalences. https://arxiv.org/abs/math/0401242

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