L1-Algebra of a Locally Compact Groupoid. (14th June 2011)

• Record Type: Journal Article
• Authors: Amini, Massoud; Medghalchi, Alireza; Shirinkalam, Ahmad
• Other Names: Rangipour B. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2011(2011)
• Publication Date: 2011-06-14
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2011/856709
• Languages: English
• ISSNs: 2090-6285

Abstract

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 ).