PlanetPhysics/Fourier Stieltjes Algebra of a Groupoid 2

The Fourier-Stieltjes algebra of a groupoid, $G_l$ . In ref. ), A.L.T. Paterson defined the Fourier-Stieltjes algebra of a groupoid , $G_l$, as the space of coefficients $\varphi =(\xi ,\eta )$, where $\xi ,\eta$ are $L^{\mathrm{\infty }}$-sections for some measurable $G_l$ -Hilbert bundle $(\mu ,\mathrm{\Re },L)$. Thus, for $x\in G_l$,

$\varphi (x)=L(x)\xi (s(x),\eta (r(x))).$

Therefore, $\varphi$ belongs to $L^{\mathrm{\infty }}{G}_l=L^{\mathrm{\infty }}(G_l,\nu )$.