Convolution algebras for topological groupoids with locally compact fibres

• Autorzy: Buneci M. R.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to introduce various convolution algebras associated with a topological groupoid with locally compact fibres. Instead of working with continuous functions on G, we consider functions having a uniformly continuity property on fibres. We assume that the groupoid is endowed with a system of measures (supported on its fibres) subject to the "left invariance" condition in the groupoid sense.

Słowa kluczowe

EN

convolution algebra; groupoid; uniform continuity; Haar system

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 2
• Strony: 159--172
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Buneci M. R.

• Constantin Brâcusi University of Tâgu-Jiu Str. Geneva, Nr. 3, 210136 Tâgu-Jiu, Romania,

Bibliografia

• [1] M. Buneci, Haar systems and homomorphism on groupoids, Operator Algebras and Mathematical Physics (Constanta, 2001), 35–49, Theta, Bucharest, 2003.
• [2] A. Connes, Sur la theorie noncommutative de l’integration, Lecture Notes in Math.,Springer-Verlag, Berlin 725 (1979), 19–143.
• [3] G. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134–165.
• [4] G. Mackey, Ergodic theory, group theory and differentiall geometry, Proc. Nat. Acad. Sci. USA 50 (1963), 1184–1191.
• [5] M. Khoshkam, G. Skandalis, Regular representation of groupoid C*-algebras and applications to inverse semigroups, J. Reine Angew. Math. 546 (2002), 47–72.
• [6] P. Hahn, Haar measure for measure groupoids, Trans. Amer. Math. Soc. 242 (1978), 1–33.
• [7] A. Ramsay, Topologies on measured groupoids, J. Funct. Anal. 47 (1982), 314–343.
• [8] J. Renault, A groupoid approach to C*-algebras, Lecture Notes in Math., Springer-Verlag, 793, 1980.
• [9] J. Renault, The ideal structure of groupoid crossed product algebras, J. Operator Theory 25 (1991), 3–36.
• [10] A.K. Seda, A continuity property of Haar systems of measures, Ann. Soc. Sci. Bruxelles 89 IV (1975), 429–433.
• [11] A.K. Seda, On the continuity of Haar measure on topological groupoids, Proc. Amer. Math. Soc. 96 (1986), 115–120.
• [12] J.L. Tu, Non-Hausdorff groupoids, proper Actions and K-theory, Doc. Math. 9 (2004), 565–597.
• [13] J. Westman, Nontransitive groupoid algebras, Univ. of California at Irvine, 1967.
• [14] J. Westman, Harmonic analysis on groupoids, Pacific J. Math. 27 (1968), 621–632.