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Aug 13, 2013 at 14:54 vote accept Murat Güngör
Aug 13, 2013 at 14:54 comment added Murat Güngör By the way, I realized that the inclusion $\supseteq$ in my question (more generally, the inclusion $\supseteq$ in the first displayed equality on p. 114 of Poulsen's) follows easily from Lemma 3.13 of Knapp's as well.
Aug 13, 2013 at 14:50 comment added Murat Güngör You are right. My computation above is definitely incorrect. Thanks for the clarification.
Aug 13, 2013 at 14:16 comment added Francois Ziegler @MuratGüngör: Yes, I am sure. (Your formula for $(Xf)(x)$ has a stray $x$; compare my edited answer.)
Aug 13, 2013 at 14:14 history edited Francois Ziegler CC BY-SA 3.0
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Aug 12, 2013 at 14:06 comment added Murat Güngör Thank you for the reference, but are you sure that Poulsen's results imply my equality? In his notation (see p. 113), we have $(Xf)(x)=-Xxf'(x)$ for $X\in\mathrm{Lie}(\mathbb{R})$, so $X$ is not simply the derivative operator; consequently, the right-hand side of the first displayed equality on his p. 114 is not my right-hand side above.
Aug 7, 2013 at 20:22 history edited Francois Ziegler CC BY-SA 3.0
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Aug 6, 2013 at 18:30 history answered Francois Ziegler CC BY-SA 3.0