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
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I tried to do it. But not sure what to do.