Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that
is real-valued for all f in H.
Recall that if T:H to H is a bounded linear operator on the Hilbert space H then there
exists a unique and bounded linear operator T^* such that
T^* : H to H
and for all g ...
It is proven that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H, where (f,f) denotes the inner product on H.
The solution is detailed and well presented.