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Jun 7, 2012 at 13:10 comment added Martin Wanvik Great! Thanks, Nik. For posterity, I'll add the exact reference to Takesaki's book: theorem 4.2 and proposition 4.6 in chapter III (I actually did ask someone else about this prior to posting here on MO, and was pointed in this direction - what I failed to notice, however, was the equality $\| \omega \| = \| \phi \|$, and ended up with the estimate $\| \varphi \| \geq |\varphi(1)| = |\langle \pi(v)\xi,\xi \rangle|$, rather than $\| \varphi \| \geq \omega(1) = \| \xi\|^2$).
Jun 6, 2012 at 17:39 history edited Nik Weaver CC BY-SA 3.0
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Jun 6, 2012 at 16:33 vote accept Martin Wanvik
Jun 6, 2012 at 16:04 history undeleted Nik Weaver
Jun 6, 2012 at 16:04 history edited Nik Weaver CC BY-SA 3.0
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Jun 6, 2012 at 15:58 history deleted Nik Weaver
Jun 6, 2012 at 15:58 history answered Nik Weaver CC BY-SA 3.0