Let H be a Hilbert space, with a in H and b in H.
Let u be an operator on H with u(x)=<b,x>a
Find the adjoint of u.
The Attempt at a Solution
<ux,y>=<<b,x>a,y> = <b,x><a,y> = <b<a,y>,x>
So it seems that all I need to do is flip that last inner product round. But that will introduce a complex conjugate, stopping me from getting the equation to the right form (maybe?).