# Thread: inner product

1. ## 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!

2. Originally Posted by mivanova
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).