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In article
<20051102.1146339208262.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Cathy <cathy218@xxxxxxxxx> wrote:
> Hello, all.
> I am doing a problem and have some trouble with it. Any idea is greatly
> appreciated.
> T is a linear operator from normed linear space X to a norm linear space Y.
> I need to prove
> ||T|| = Sup{<Tx,y*>: ||x||<=1,||y*||<=1,x in X, y* in Y*}
>
> It is easy to get ||T||>= Sup<Tx,y*>. But the other direction of the
> inequality troubles me.
HInts: 1. There exists x with ||x|| <= 1 such that Tx is near
||T||. 2. Given y in Y, there exists f in Y* such that ||f|| = 1
and f(y) = ||y|| (consequence of Hahn-Banach).
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