Compact Linear Transformation is Bounded
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
Theorem
Let $H, K$ be Hilbert spaces.
Let $T \in B_0 \left({H, K}\right)$ be a compact linear transformation.
Then $T$ is also a bounded linear transformation.
That is, $B_0 \left({H, K}\right) \subseteq B \left({H, K}\right)$.
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $II.4.2(a)$