Let $T : X \to X$ be a measure-preserving transformation and $U\_T : L^2(X, \mu) \to L^2(X, \mu)$ , $(U\_T f) (x) = f(Tx).$

What does it mean a $\bf{simple}$ eigenvalue of $U\_T$?

$\lambda \in \mathbb{C}$ is an eigenvalue of $U\_T$ if $\exists f \in L^2(X, \mu), f \neq 0$ such that $U\_T f = \lambda f$.

What does it mean, in this particular case, that $\lambda$ is simple? 

Thank you!