2004/01/19 by Huaxin Lin, Lin, Huaxin · 4 citations
Mathematics · #46L05 #46L35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Algebra over a field #FOS: Mathematics #Holomorphic and Operator Theory #Law #Mathematics #Operator Algebras (math.OA) #Political science #Pure mathematics #Unitary state #math.OA #msc:46L05 #msc:46L35
paper · pdf · doi:10.48550/arxiv.math/0401242
published in arXiv (Cornell University) (Cornell University)
arxiv created 2004/01/19 · openalex publication_date 2004/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let A be a unital separable amenable \CA and C be a unital \CA 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 \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).