Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-27T01:58:58.763Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stone-Čech compactification of Prim A

Published online by Cambridge University Press:  17 April 2009

May Nilsen
May Nilsen
Affiliation:
Department of MathematicsThe University of NewcastleCallaghan NSW 2308Australia, e-mail: may@frey.newcastle.edu.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a C*-algebra A, we give simple proofs of the following: Cb (Prim A) is isomorphic to the centre ZM(A) of the multiplier algebra, Cb (Prim A) is isomorphic to C (Prim M(A)) and Prim ZM(A) is the Stone-Čech compactification of Prim A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 3 , December 1995 , pp. 377 - 383
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Becker, T., ‘A few remarks on the Dauns-Hofmann theorems for C*-algebras’, Arch. Math. 43 (1984), 265–269.Google Scholar
[2]Dauns, J. and Hofmann, K.H., ‘Representations of rings by sections’, Mem. Amer. Math. Soc. 83 (1968).Google Scholar
[3]Dixmier, J., ‘Ideal center of a C*-algebra’, Duke Math. J. 35 (1968), 375–382.CrossRefGoogle Scholar
[4]Dixmier, J., C*-algebras (North-Holland, New York, 1977).Google Scholar
[5]Gootman, E.C. and Lazar, A.J., ‘Crossed products of type I AF algebras by abelian groups’, Israel J. Math. 56 (1986), 267–279.CrossRefGoogle Scholar
[6]Green, P., ‘The local structure of twisted covariance algebras’, Acta Math. 140 (1978), 191–250.CrossRefGoogle Scholar
[7]Nilsen, M., ‘C*-bundles’, (preprint, 1995).Google Scholar
[8]Pedersen, G., ‘Applications of weak* semicontinuity in C*-algebra theory’, Duke Math. J. 39 (1972), 431–450.CrossRefGoogle Scholar
[9]Semadeni, Z., Banach spaces of continuous functions, Volume 1 (PWN, Polish Scientific, Warsaw, 1971).Google Scholar
[10]Walker, R.C., The Stone-Čech compactification (Springer Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar