Recent content by just.so

Since the given limit exists for all y \in H , we have lim_{x \rightarrow \infty} \langle x_{n},y \rangle is a function from H into C (or R). With a little messy manipulation (reversing of the inner product - which I think I can "unreverse" at the end) it is quite easy to show that it (the...

Good point! Have had a growing suspicion that it would not converge (strongly) otherwise the question would have been "show there exists x \in H such that x_n \rightarrow x " as opposed to asking to show weak convergence only. Grrr... But thanks for the counter example, Dick. Hmmm... back to...

Very definitely general... Will try out your suggestions though.

Again, many thanks!

Thanks Hurkyl. That is what I was trying to use, but I hadn't managed to convince myself that I could replace the equality with a limit.

Homework Statement Let H be a Hilbert space. Prove that if \left\{ x _{n} \right\} is a sequence such that lim_{n\rightarrow\infty}\left\langle x_{n},y\right\rangle exists for all y\in H, then there exists x\in H such that lim_{n\rightarrow\infty} \left\langle x_{n},y\right\rangle =...

That IS sweet! A gazillion thanks! J

[SOLVED] Sequences in lp spaces... (Functional Analysis) Homework Statement Find a sequence which converges to zero but is not in any lp space where 1<=p<infinity. Homework Equations N/A The Attempt at a Solution I strongly suspect 1/ln(n+1) is a solution. Since ln(n+1) ->...