Timeline for Can a non-commutative C*-algebra be a minimal operator space?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2014 at 10:24 | comment | added | Mateusz Wasilewski | @NarutakaOZAWA: Thank you very much. | |
| Jan 25, 2014 at 8:06 | comment | added | Narutaka OZAWA | @Mateusz Wasilewski: $A$ is cb isomorphic to min iff it is subhomogeneous. A $\mathrm{C}^*$-algebra $A$ is said to be subhomogeneous if it has only finite-dimensional irreducible representations (which is also equivalent to that it is isomorphic to a subalgebra of $M_n(C(X))$). Indeed, if $A$ is not subhomogeneous, then $A^{**}$ has a direct summand isomorphic to $B(H)$ with infinite-dimensional $H$, which is not cb isomorphic to a min space. | |
| Jan 24, 2014 at 16:32 | vote | accept | Mateusz Wasilewski | ||
| Jan 24, 2014 at 16:31 | comment | added | Mateusz Wasilewski | Thank you very much; this settles the completely isometric case. The completely bounded case, as it stands, is obviously false since $M_2 \oplus L_{\infty}$ (just to have it infinite dimensional) provides a (trivial) counterexample. | |
| Jan 24, 2014 at 16:01 | history | answered | Caleb Eckhardt | CC BY-SA 3.0 |