L1-Algebra of a Locally Compact Groupoid. (14th June 2011) - Amini, Massoud; Medghalchi, Alireza; Shirinkalam, Ahmad
Abstract : For a locally compact groupoidG with a fixed Haar systemλ and quasi-invariant measureμ, we introduce the notion ofλ -measurability and construct the spaceL 1 (G, λ, μ ) of absolutely integrable functions onG and show that it is a Banach∗ -algebra and a two-sided ideal in the algebraM (G ) of complex Radon measures onG . We find correspondences between representations ofG on Hilbert bundles and certain class of nondegenerate representations ofL 1 (G, λ, μ ).