norm of a linear operator and dual
- From: Cathy <cathy218@xxxxxxxxx>
- Date: Sat, 29 Apr 2006 15:32:58 EDT
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.
Cathy
.
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