Timeline for Calkin Algebra and the embedding
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2013 at 12:42 | comment | added | Tomasz Kania | Oh yes, if $K$ is a non-separable Hilbert space, then $B(K)$ contains $\ell_\infty(\omega_1)$ which has no strictly convex renorming by a result of Mahlon Day. | |
| Dec 15, 2013 at 12:41 | comment | added | Johannes Hahn | So that strictly convex renorming exists only in the separable case? I wasn't aware of that. | |
| Dec 15, 2013 at 12:36 | comment | added | Johannes Hahn | There's something wrong here: The calkin algebra is a C* algebra and can therefore be embedded into a $B(\tilde{H})$ for some big enough hilbert space $\tilde{H}$. The point of the question is that one cannot take $\tilde{H}=H$. | |
| Dec 15, 2013 at 12:21 | history | answered | Tomasz Kania | CC BY-SA 3.0 |