Nonzero Eigenvalue of Compact Operator has Finite Dimensional Eigenspace

Theorem
Let $H$ be a Hilbert space.

Let $T \in B_0 \left({H}\right)$ be a compact operator.

Let $\lambda \in \sigma_p \left({T}\right), \lambda \ne 0$ be a nonzero eigenvalue of $T$.

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