Give an example of a non-self-adjoint operator on a Hilbert space $H$ whose range is $H$ and which is not invertible.
I cannot think of an example to save my life. Any solutions/hints are greatly appreciated.
Give an example of a non-self-adjoint operator on a Hilbert space $H$ whose range is $H$ and which is not invertible.
I cannot think of an example to save my life. Any solutions/hints are greatly appreciated.
How about the shift map on $\ell^2(\mathbb{N})$?