A Classification Theorem for Nuclear Purely Infinite Simple C*-Algebras
| dc.creator | Phillips, N. Christopher | |
| dc.date | 1995-07-01 | |
| dc.date | 1997-12-18 | |
| dc.date.accessioned | 2026-07-07T08:59:17Z | |
| dc.date.available | 2026-07-07T08:59:17Z | |
| dc.description | Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A is isomorphic to A if in addition A is purely infinite, we prove that KK-equivalence implies isomorphism for nonunital separable nuclear purely infinite simple C*-algebras. It follows that if A and B are unital separable nuclear purely infinite simple C*-algebras which satisfy the Universal Coefficient Theorem, and if there is a graded isomorphism from K_* (A) to K_* (B) which preserves the class of the identity, then A is isomorphic to B. Our main technical results are, we believe, of independent interest. We say that two asymptotic morphisms t ---> ϕ_t and t ---> ψ_t from A to B are asymptotically unitarily equivalent if there exists a continuous unitary path t ---> u_t in the unitization B^+ such that || u_t ϕ_t (a) u_t^* - ψ_t (a) || ---> 0 for all a in A. Let A be separable, nuclear, unital, and simple, and let D be unital. We prove that any asymptotic morphism from A to K tensor O_infinity tensor D is asymptotically unitarily equivalent to a homomorphism, and two homotopic homomorphisms from A to K tensor O_infinity tensor D are asymptotically unitarily equivalent. | |
| dc.description | LaTeX, 48 pages (in 10pt type). This revision incorporates four modifications. First, there is now a preprint containing the theorems from which the present paper starts (funct-an/9712002). Second, the proofs have been slightly simplified (eliminating "local asymptotic morphisms"). Third, a section containing some nonclassification results in the nonnuclear case has been added. Fourth, some misprints have been corrected | |
| dc.identifier | https://arxiv.org/abs/funct-an/9506010 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9506010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147655 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L35 (Primary) 19K99, 46L80 (Secondary) | |
| dc.title | A Classification Theorem for Nuclear Purely Infinite Simple C*-Algebras | |
| dc.type | text |