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Aug 19, 2013 at 15:10 comment added Sebastien Palcoux I have posted a specification here.
Aug 19, 2013 at 9:41 vote accept Sebastien Palcoux
Aug 19, 2013 at 9:22 comment added Dan Petersen Oh, I missed the condition on the dimension of $X_n$. I modified my example by your suggestion, Johannes.
Aug 19, 2013 at 9:20 history edited Dan Petersen CC BY-SA 3.0
added 29 characters in body
Aug 19, 2013 at 9:15 comment added Johannes Ebert But you can take $H=R^{\infty}$ and $H_n =R^{n-1}$ instead.
Aug 19, 2013 at 9:11 comment added Sebastien Palcoux oups... your $X_{n}$ is not $n$-dimensional.
Aug 19, 2013 at 8:55 vote accept Sebastien Palcoux
Aug 19, 2013 at 9:09
Aug 19, 2013 at 8:53 history answered Dan Petersen CC BY-SA 3.0