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Math Help - inner product

  1. #1
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    inner product

    Please, help me
    Let V and W be inner product spaces over F, and let T:V->W is linear. If there is an adjoint map T*:W->V such that <T(v),w>=<v,T*(w)> for all v in V and all w in W, show that T* is in L(W,V).
    Thank you!
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  2. #2
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    Quote Originally Posted by mivanova View Post
    Please, help me
    Let V and W be inner product spaces over F, and let T:V->W is linear. If there is an adjoint map T*:W->V such that <T(v),w>=<v,T*(w)> for all v in V and all w in W, show that T* is in L(W,V).
    Thank you!
    Have you made no start on this at all? What does L(W,V) mean? In order to show that T* is in L(W,V) all you have to do is show that T* satisfies the conditions specified in the definition of L(W,V).
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