Adjoint of Finite Rank Operator
Theorem
Let $H, K$ be Hilbert spaces.
Let $T \in B_{00} \left({H, K}\right)$ be a bounded finite rank operator.
Then $T^* \in B_{00} \left({K, H}\right)$, i.e., the adjoint of $T$ is also a bounded finite rank operator.
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) $\text{II}.4$ Exercise $3$
