A Classification Theorem for Nuclear Purely Infinite Simple C -Algebras 1

摘要: Starting from Kirchberg's theorems announced at the operator algebra conference in Gen eve 1994, namely O2 A = for separable unital nuclear simple and O1 purely innite A; we prove that KK-equivalence implies isomorphism nonunital C -algebras. It follows if B are -algebras which satisfy Universal Coecien t Theorem, there is a graded fromK (A) to K (B) preserves K0-class of identity, then B: Our main technical results are, believe, independent in- terest. We say two asymptotic morphisms 7! 't asymptotically unitarily equivalent exists continuous unitary path ut unitization + such kut't(a)ut t(a)k ! 0 all A: following on deformations equivalence. Let be separable, nuclear, unital, simple, let D unital. Then any morphism equiv- alent homomorphism, homotopic homomorphisms necessarily equivalent. also give some nonclassication nonnuclear case. 1991 Mathematics Subject Classication: Primary 46L35; Secondary 19K99, 46L80.