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 $$\phi = (\xi,\eta)$$, where $$\xi,\eta$$ are $$L^{\infty}$$-sections for some measurable $$G_l$$ -Hilbert bundle $$(\mu,\Re,L)$$. Thus, for $$x \in G_l$$, $$ \phi(x) = L(x) \xi (s(x),\eta (r(x))). $$

Therefore, $$\phi$$ belongs to $$L^\infty{G_l} = L^\infty({G_l},\nu)$$.