Talk:Weak convergence (Hilbert space)

From Wikipedia, the free encyclopedia

[edit] Weak convergence of orthonormal sequences

The current proof assumes that the sequence converges weakly (and then shows that it has to converge to 0 in this case). But how do you know that the sequence converges weakly in the first place?

Also, is the weak limit unique in general (in some suitable sense of what unique means)? Simon Lacoste-Julien 22:18, 25 March 2006 (UTC)

the version i am looking at does not do what you say. the claim is that any orthonomal sequence converges weakly and its weak limit is the 0 vector. and yes, the weak limit is unique, as the weak topology is Hausdorff. Mct mht 13:33, 28 June 2006 (UTC)