 Adjoint operator

For $T\in L(H)$, the adjoint $T^{\ast }$ is the unique bounded operator satisfyingRiesz representation applied for each $y$ proves existence; in an orthonormal basis its matrix is the conjugate transpose of the matrix of $T$.

Given a linear operator $A$ over a space $S$ that has a inner product defined, we define the adjoint operator $A^{†}$ (the $†$ symbol is called "dagger") as the unique operator that satisfies: