Let V be an inner product space and y,z be in V. Let T be a linear operator on V defined by T(x) = <x,y>z for all x in V. Find the explicit expression for T*.

I know that <T(x),w> = <x,T*(w)>.

Hence, <<x,y>z,w> = <x,T*(w)>. But <x,y> is just a scalar.

Then, <x,y><z,w> = <x,T*(w)>.

But how do i proceed on from here to find T*?

Thank you.