Definition 0.1. The Fourier-Stieltjes algebra of a groupoid, Gl. In ref. [3]), A.L.T. Paterson
defined the Fourier-Stieltjes algebra of a groupoid, Gl, as the space of coefficients ϕ = (ξ,η),
where ξ,η are L∞-sections for some measurable G
l -Hilbert bundle (μ,ℜ,L). Thus, for
x ∈ Gl,
Therefore, ϕ belongs to L∞G
l = L∞(G
l,ν).
References
[1] A. Ramsay and M. E. Walter, Fourier-Stieltjes algebras of locally compact groupoids,
J. Functional Anal. 148: 314-367 (1997).
[2] A. L. T. Paterson, The Fourier algebra for locally compact groupoids., Preprint,
(2001).
[3] A. L. T. Paterson, The Fourier-Stieltjes and Fourier algebras for locally compact
groupoids, (2003).
