Hi, I am wondering what mistake i might have made in the following. (v, Au) = [(v, Au)*]* = [(A†v, u)*]* = (u, A†v)* = ((A†)†u, v)* = (v, (A†)†u), where v and u are arbitrary vectors in a Hilbert space. That proves that A = (A†)†, doesn't it? My tutor says some of the steps are wrong. What might those be?