Hi all !!

Someone can show me if that demonstration is going right ??

Let A, B self adjoint operators such that AB = BA. Show that exist unique ortonormal base that diagonalize simultaneously A and B.

Solution:

How AB = BA then A and B are commutative operators. Let an eigenvalue of A and the self space associate. Let such that:

Then

Then is invariant by B. Then v is an eigenvector common the A and B, then:

But in this point my demonstration becomes strange, because I assume that exist , but I'm not sure that is correct...

One more time, thanks a lot...