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Apr 18, 2012 at 10:53 comment added Olaf Kummers Sure, sorry. :)
Apr 18, 2012 at 10:03 comment added Yemon Choi @Olaf: I meant the particular P in my answer, I thought that was obvious from context
Apr 18, 2012 at 8:43 comment added Olaf Kummers What do you mean both? One of them can be e.g. $\ell_\infty$.
Apr 18, 2012 at 7:09 comment added Yemon Choi @Olaf: without thinking about it too hard, I can at least point you to a result of Blower mentioned here mathoverflow.net/questions/12211/… which implies, in particular, that either $P(B(H))$ or $(I-P)(B(H))$ is isomorphic as a Banach space to $B(H)$. I rather suspect both are, but don't see at this moment how one would show this.
Apr 18, 2012 at 6:41 comment added Olaf Kummers Thanks. How about (Banach) complemented subspaces (Banach) isomorphic to $\mathcal{K}(H)$ or $\mathcal{B}(H)$?
Apr 17, 2012 at 21:56 vote accept Olaf Kummers
Apr 17, 2012 at 21:46 history answered Yemon Choi CC BY-SA 3.0