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

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

  2. If we have a negative-semidefinite operator, what kinds of perturbations will result in selfnegative-adjointsemidefinite 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.

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

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

  2. If we have a negative-semidefinite operator, what kinds of perturbations will result in self-adjoint 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.

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

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

  2. 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.

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  • 21
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Perturbations of positive-definite self-adjoint operators

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

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

  2. If we have a negative-semidefinite operator, what kinds of perturbations will result in self-adjoint 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.