2004/01/19 by Huaxin Lin, Lin, Huaxin
Mathematics · #46L05 #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L35
paper · pdf · doi:10.48550/arxiv.math/0401241
to appear Canad J. Math
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 2026/07/28
Let A be an amenable separable \CA and B be a non-unital but σ-unital simple \CA with continuous scale. We show that two essential extensions τ1 and τ2 of A by B are approximately unitarily equivalent if and only if [τ1]=[τ2] \rm in KL(A, M(B)/B). If A is assumed to satisfy the Universal Coefficient Theorem, there is a bijection from approximate unitary equivalence classes of the above mentioned extensions to KL(A, M(B)/B). Using KL(A, M(B)/B), we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions.