So here is my question,
Let $H$ be a Hilbert-space and $K:H\rightarrow H$ a compact operator. I know that if $K$ is self adjoint, then it has one eigenvalue $\mu$ such that $|\mu|=||K||$. Can some one give me a nice counter example of a not self adjoint compact operator such that such a eigenvalue does not exist?
Thanks in advance!