Re: norm of a linear operator and dual
- From: A N Niel <anniel@xxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 29 Apr 2006 16:27:33 -0400
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.
Cathy
How about the identity operator, can you do that one?
.
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- From: Cathy
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