Timeline for Commutative direct summands of C*-algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2018 at 6:33 | comment | added | Marten Wortel | I assumed the original question referred to algebra direct summands. | |
| Oct 25, 2018 at 11:25 | comment | added | Tomasz Kania | If you only require a complemented subalgebra then the diagonal matrices are such a summand too. | |
| Oct 25, 2018 at 6:14 | comment | added | Marten Wortel | The bidual of $C[0,1]$ is indeed much bigger, but its atomic part is $\ell_\infty[0,1]$. And the atomic part is a direct summand, so a direct summand of the atomic part is a direct summand of the bidual. I have to go to matrices in order to make sure that $A$ has no commutative direct summand; the problem with $C[0,1]$ is that it is commutative, so it has a commutative direct summand. | |
| Oct 24, 2018 at 17:28 | comment | added | Tomasz Kania | It is not clear to me that your description of the bidual is accurate since $C[0,1]^{**}$ is much larger than $\ell_\infty[0,1]$. Also, what is the gain of going from $C[0,1]$ to matrices? | |
| Oct 24, 2018 at 17:26 | vote | accept | Mark Roelands | ||
| Oct 24, 2018 at 12:35 | history | answered | Marten Wortel | CC BY-SA 4.0 |