Timeline for $C^*$-algebra which is not von Neumann, but satisfies the property that ever self-adjoint element is
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2017 at 6:57 | vote | accept | user860374 | ||
| Sep 21, 2017 at 0:00 | comment | added | Caleb Eckhardt | The definition you are looking for is "real rank 0"(RR0). It was introduced by L.Brown and Pedersen (JFA 1991)--see Theorem 2.6 especially as it pertains to your question. The class of (non von Neumann) RR0 C*-algebras is rich. As a first class of examples, all AF algebras (inductive limits of finite dimensional C*-algebras) have RR0 (this is easy to see directly since the class of algebras you wish to describe is clearly closed under injective inductive limits). If you're interested in more examples you cansearch for "simple AT algebras" which will probably lead you to even more examples. | |
| Sep 20, 2017 at 12:33 | answer | added | Simon Henry | timeline score: 3 | |
| Sep 20, 2017 at 12:13 | answer | added | Nik Weaver | timeline score: 3 | |
| Sep 20, 2017 at 8:09 | history | asked | user860374 | CC BY-SA 3.0 |