A proof that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H
Not what you're looking for? Search our solutions OR ask your own Custom question.
Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that
(Tf,f)
is real-valued for all f in H.
© BrainMass Inc. brainmass.com December 24, 2021, 4:45 pm ad1c9bdddfhttps://brainmass.com/math/matrices/proof-self-adjoint-linear-operator-5497
Solution Preview
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 ...
Solution Summary
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.
$2.49