Nonzero Eigenvalue of Compact Operator has Finite Dimensional Eigenspace

Theorem
Let $H$ be a Hilbert space.

Let $T \in \map {B_0} H$ be a compact operator.

Let $\lambda \in \map {\sigma_p} T, \lambda \ne 0$ be a nonzero eigenvalue of $T$.

Then the eigenspace for $\lambda$ has finite dimension.