Definition:Adjoint Linear Transformation

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Let $H, K$ be Hilbert spaces.

Let $A \in \map B {H, K}$ be a bounded linear transformation.

Let $B \in \map B {K, H}$ be the unique bounded linear transformation provided by Existence and Uniqueness of Adjoint.

Then $B$ is called the adjoint of $A$, and denoted $A^*$.

The operation of assigning $A^*$ to $A$ may be referred to as adjoining.

Also see

  • Results about adjoints can be found here.