- #1

- 5

- 0

If T is a bounded linear operator on a Hilbert space, what can we say about the spectra of T and T* ([itex]\sigma(T)=\{\lambda:T-\lambda I[/itex] is not invertible})?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter pyf
- Start date

- #1

- 5

- 0

If T is a bounded linear operator on a Hilbert space, what can we say about the spectra of T and T* ([itex]\sigma(T)=\{\lambda:T-\lambda I[/itex] is not invertible})?

- #2

- 5

- 0

- #3

- 13,033

- 588

- #4

mathwonk

Science Advisor

Homework Helper

2020 Award

- 11,123

- 1,323

Is it true at least for normal operators that the spectral radii are the same?

- #5

Landau

Science Advisor

- 905

- 0

Yes, then they are the same. A general theorem says that for a normal element x in a C*-algebra, its spectral radius equals its norm. Since x and x* have the same norm, they have the same spectral radius.

Share: