Adjoint of Finite Rank Operator
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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
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Sources
- 1990: John B. Conway: A Course in Functional Analysis ... (previous) ... (next) $\text{II}.4$ Exercise $3$
