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Thread: inner product space question

  1. December 3rd 2009, 06:48 PM #1
    dannyboycurtis
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    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}^*?
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  2. December 3rd 2009, 07:15 PM #2
    NonCommAlg
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    Quote Originally Posted by dannyboycurtis View Post
    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: <U_2x,y>=<TT^*x,y>=<T^*x,T^*y>=<x,TT^*y>=<x,U_2y >. the proof for U_1 is the same.
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