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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})?

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- Thread starter pyf
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- #1

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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})?

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

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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.

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