= Weighted Hilbert structure of velocity-reset relaxation
{title2=$H=L^2(M^{-1}dv),\quad\Pi f=\left(\int f\right)M$}
For $M>0$ with <integral> one, the <Cauchy-Schwarz inequality> makes the mass functional bounded on the weighted <Hilbert space>. The vector $M$ has <norm> one, so the velocity-reset projection is the <orthogonal projection> onto its span. Consequently $L=\Pi-I$ is bounded and <self-adjoint>. This Hilbert geometry differs from the norm-one positive reset projection on phase-space $L^1$.
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