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


Sources