Compact Hermitian Operator has Countable Point Spectrum

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 theorem You 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) $\text {II}.5.1$