I think that the solution is:
|\left\langle f^n-f,cosh \right\rangle| \le \|f^n-f\|\|cosh\|
But \forall \epsilon \ \ \exists n_o(\epsilon) such that for any
n \ge n_0(\epsilon) we have that:
|\left\langle f^n-f,cosh \right\rangle| \le \epsilon \|cosh\|
Therefore \left\langle...
You are right, I was wrong about that.
Ok, that was my thought from the very beginning. But if I need just the f(1)=0, then how do I know that the limit f is also a continuous differentiable function? Don't I need that as well?
Hi! I have used the physics forum a lot of times to deal with several tasks that I had and now its the time to introduce my own query! So please bear with me :-)
Homework Statement
Equip the set C^1_{[0,1]} with the inner product:
\left\langle f,g \right\rangle= \int_{0}^{1}...