Let be a Hilbert space and suppose . Then for all with .
please! ... I don't understand its.
Thank you so much. I think it is easily proof, when you show for me.
By the way, I have other proof of this theorem . Can you check it for me?
From Parallelogram Law, we have
That is
or --------(*)
Now take inferior limit as (*), we have
Since , we obtains that
It follow from above and our assumption ; , that
Thus, there is a positive integer such that , for all
Consider, for all
we can put
This implies that
or
Taking the inferior limit, we get
and so
Thus
It follows that and hence
#
I tried to do it. But not sure what to do.