= Ellipticity of a bounded Hilbert-space operator
{title2=$\operatorname{Re}\langle Lv,v\rangle\geq\gamma\|v\|^2$}
In a variational <Hilbert space> setting, a bounded operator $L$ is elliptic or uniformly coercive when $\operatorname{Re}\langle Lv,v\rangle\geq\gamma\|v\|^2$ for a constant $\gamma>0$. On a real <Hilbert space> this condition depends on the symmetric part of $L$ and does not imply <self-adjointness>. It differs from the principal-symbol condition defining an <elliptic differential operator>.
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