Closure of Range of Compact Linear Transformation is Separable

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

This theorem requires a proof. 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) $II.4.5$