Timeline for Do c.p.c. order zero maps between local C*-algebras map C*-subalgebras to C*-subalgebras?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2015 at 15:15 | vote | accept | Phoenix87 | ||
| May 4, 2015 at 12:27 | answer | added | Hannes Thiel | timeline score: 4 | |
| Mar 13, 2015 at 9:57 | comment | added | Phoenix87 | Completely positive contractive | |
| Mar 13, 2015 at 6:08 | comment | added | Zbigniew | @Phoenix87 What is the acronym c.p.c in the question. | |
| Mar 11, 2015 at 20:57 | comment | added | Leonel Robert | The closed subspaces $\phi^{-1}(B_1)\cap A_n$, $\phi^{-1}(B_2)\cap A_n$... would cover $A_n$ so one of them would have to agree with it by Baire's theorem. | |
| Mar 11, 2015 at 13:14 | comment | added | Phoenix87 | @ChrisHeunen The definition of local C*-algebra I would like to consider for this question is given in the OP. As a special example you can consider inductive limits of C*-algebras (where for simplicity you can take, say, injective connecting maps, although this shouldn't be strictly necessary), but you omit the completion w.r.t to the norm in order to remain with a pre-C*-algebra. In the above example, $M_\infty$ can be constructed this way from the sequence of matrix algebras $M_n(\mathbb C)$ with obvious inclusions, whose C*-limit is the C*-algebra of compact operators. | |
| Mar 11, 2015 at 12:55 | comment | added | Chris Heunen | By local C*-algebra, do you mean a local pre-C*-algebra that is complete, i.e. a directed colimit in the category of C*-algebras and $*$-homomorphisms? Wouldn't any C*-algebra satisfy that (taking $\{A_i\}=\{A\}$)? | |
| Mar 10, 2015 at 17:36 | history | asked | Phoenix87 | CC BY-SA 3.0 |