# Compact Self-Adjoint Operator has Countable Point Spectrum

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## Theorem

Let $H$ be a Hilbert space.

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

Then its point spectrum $\sigma_p \left({T}\right)$ is countable.

## Proof

## Sources

- 1990: John B. Conway:
*A Course in Functional Analysis*... (previous) ... (next) $II.5.1$