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

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- Dec 3rd 2009, 06:48 PMdannyboycurtisinner product space question
If T is a linear operator on an inner product space V and $\displaystyle U_{1}$=T+T* and $\displaystyle U_{2}$=TT*, how can I show that $\displaystyle U_{1}=U_{1}^*$ and $\displaystyle U_{2}=U_{2}^*$?

- Dec 3rd 2009, 07:15 PMNonCommAlg