Closure of Range of Compact Linear Transformation is Separable
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Theorem
Let $H, K$ be Hilbert spaces.
Let $T \in \map {B_0} {H, K}$ be a compact linear transformation.
Then $\map \cl {\Rng T}$ is separable.
Proof
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Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.4.5$