Timeline for $*$-representation $\pi:A\odot B\to B(H_1\otimes H_2)$ such that $\pi \neq \pi_1\otimes \pi_2$
Current License: CC BY-SA 3.0
3 events
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| Sep 5, 2016 at 14:16 | comment | added | Stefan Waldmann | @Transcendental I was a bit sloppy, the composition is meant as you say. If the projections $P$ and $Q$ are rank one, then the $\pi_1$ and $\pi_2$ are well-def, ie. consistently defined. | |
| Sep 5, 2016 at 3:27 | comment | added | Transcendental | Dear Dr Waldmann. Could you kindly provide some clarification? Do you mean $$ \pi(a \otimes 1_{B}) \circ ({\operatorname{Id}_{\mathcal{H}_{1}}} \otimes Q) = {\pi_{1}}(a) \otimes Q $$ and $$ \pi(1_{A} \otimes b) \circ (P \otimes \operatorname{Id}_{\mathcal{H}_{2}}) = P \otimes {\pi_{2}}(b) $$ in the second paragraph? I don’t see how one can compose $ \pi(a \otimes 1_{B}) $ with $ Q $ alone, or $ \pi(1_{A} \otimes b) $ with $ P $ alone. Finally, are you saying that these formulas define $ \pi_{1} $ and $ \pi_{2} $ in a consistent manner? Thank you! | |
| Aug 10, 2016 at 5:14 | history | answered | Stefan Waldmann | CC BY-SA 3.0 |