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## Homework Statement

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.

Thanks!

## Homework Equations

<ux,y>=<x,u*y>

## 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?).