Spectra of T and T* when T is a bounded linear operator

Hi,

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

I'm asking because they are equal for finite rank operators and I hope the relation is equally nice in infinite dimensions. :)

dextercioby
Homework Helper
They're not related for arbitrary operators in $\infty$-dimensional HS. If T is self-adjoint, the 2 spectra are equal.

mathwonk