# Adjoint of Finite Rank Operator

Jump to navigation
Jump to search

## 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

- 1990: John B. Conway:
*A Course in Functional Analysis*... (previous) ... (next) $\text{II}.4$ Exercise $3$