Hey /sci/, I've gotten stuck on this proof for a month now, and I need your help. I usually don't get have problems with functional analysis, but this one has really gotten me.
If an operator is self-adjoint, then it's normal, right?
Where an operator $A$ is self-adjoint if $A=A^*$ and it's normal if $AA^*=A^*A$.
I've managed to prove assuming that $A$ is compact and using the spectral decomposition, but that's as far as I got.
Any ideas? Anything? I need this for my PhD.