# inner product space question

Printable View

• Dec 3rd 2009, 07:48 PM
dannyboycurtis
inner product space question
If T is a linear operator on an inner product space V and $U_{1}$=T+T* and $U_{2}$=TT*, how can I show that $U_{1}=U_{1}^*$ and $U_{2}=U_{2}^*$?
• Dec 3rd 2009, 08:15 PM
NonCommAlg
Quote:

Originally Posted by dannyboycurtis
If T is a linear operator on an inner product space V and $U_{1}$=T+T* and $U_{2}$=TT*, how can I show that $U_{1}=U_{1}^*$ and $U_{2}=U_{2}^*$?

since $(T^*)^*=T,$ we have: $====.$ the proof for $U_1$ is the same.