May 9th, 2014, 01:07 AM  #1 
Newbie Joined: Nov 2013 Posts: 26 Thanks: 0  selfadjoint operator
Hi, T is a selfadjoint Operator on a vector space V. I have to Show that: $\displaystyle T^2=0 \Rightarrow T=0$ ... my first idea was to argue with the Eigenvalues, because if $\displaystyle \lambda $ is Eigenvalue of T then $\displaystyle \lambda^2$ is Eigenvalue of $\displaystyle T^2$ is that a possible way, because it seams a little bit weak... or is there a better way to prove it? 
May 9th, 2014, 04:54 AM  #2 
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 
Recall that $(T^2u,u)=(Tu,Tu)$.


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operator, selfadjoint 
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