User:Caliburn/s/fa/Eigenspace Corresponding to Non-Zero Eigenvalue of Compact Operator is Finite Dimensional

Theorem

Let $\struct {\HH, \innerprod \cdot \cdot_\HH}$ be a Hilbert space.

Let $T : \HH \to \HH$ be a compact Hermitian operator.

Let $\lambda$ be a non-zero eigenvalue of $T$.

Let $E_\lambda$ be the eigenspace corresponding to $\lambda$.

Then:

$\dim E_\lambda = \infty$