# Compact Hermitian Operator has Countable Point Spectrum

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## Theorem

Let $\HH$ be a Hilbert space.

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

Then its point spectrum $\map {\sigma_p} T$ is countable.

## Proof

This theorem requires a proof.In particular: Use the next result, the spectral theoremYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1990: John B. Conway:
*A Course in Functional Analysis*(2nd ed.) ... (previous) ... (next) $\text {II}.5.1$