Adjoint of a densely defined operator
= Adjoint of a densely defined operator
{title2=$\langle Tf,h\rangle=\langle f,T^*h\rangle\quad(f\in D(T))$}
For a densely defined operator on a <Hilbert space>, $h$ belongs to $D(T^*)$ exactly when the functional $f\mapsto\langle Tf,h\rangle$ is bounded in the ambient Hilbert norm on $D(T)$. Density makes its representing vector $T^*h$ unique. Differential expressions alone do not determine this domain.
// Target: analysis.bigb