I was reading Kato's book on Perturbations of Linear Operators and have the following questions:

If we have a self-adjoint operator, what kinds of perturbations (other than relatively bounded ones) will result in self-adjoint operators?

If we have a negative-semidefinite operator, what kinds of perturbations will result in negative-semidefinite operators?

I realize my question is kind of vague. I do not have a specific aim in mind, I am just trying to gain a better understanding of what perturbations can do to unbounded operators.

Thanks in advance.