Adjoint of Finite Rank Operator

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Theorem

Let $H, K$ be Hilbert spaces.

Let $T \in \map {B_{00} } {H, K}$ be a bounded finite rank operator.


Then:

$T^* \in \map {B_{00} } {K, H}$

that is, the adjoint of $T$ is also a bounded finite rank operator.


Proof


Sources