Compact Self-Adjoint Operator has Countable Point Spectrum
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
Use the next result, the spectral theorem
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Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.5.1$
