= Unbounded self-adjoint operator
{title2=$A=A^*,\quad D(A)=D(A^*)$}
= Unbounded self-adjointness
{synonym}
A densely defined <linear operator> on a complex <Hilbert space> is self-adjoint when its <adjoint operator> has exactly the same domain and agrees there. Symmetry only requires $A\subseteq A^*$ and does not guarantee self-adjointness. A self-adjoint operator is a <closed operator> with real <spectrum>. Domains matter for differential operators and unbounded <multiplication operators>.
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