Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T07:54:21.330Z Has data issue: false hasContentIssue false
  • English
  • Français

The Primitive Ideal Space of a C*-Algebra

Published online by Cambridge University Press:  20 November 2018

John Dauns
John Dauns*
Affiliation:
Tulane University, New Orleans, Louisiana
Rights & Permissions [Opens in a new window]

Extract

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.

The commutative Gelfand-Naimark Theorem says that any commutative C*-algebra A is isomorphic to the ring C0(M, C) of all continuous complex-valued functions tending to zero outside of compact sets of a locally compact Hausdorff space M. A very important part of this theorem is an intrinsic and also a complete characterization of M as exactly the primitive ideal space of A in the hull-kernel (or weak-star) topology. In the non-commutative case, A ≌ Γ0(M, E)—the ring of sections tending to zero outside of compact subsets of a locally compact Hausdorff space M with values in the stalks or fibers E.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 42 - 49
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Busby, R., Double centralizers and extensions of C*-algebras, Trans. Amer. Math. Soc. 132 (1968), 79–99.Google Scholar
2. Busby, R., On structure spaces and extensions of C*'-algebras, J. Functional Analysis 1 (1967), 370–377.Google Scholar
3. Busby, R., Extensions in certain topological algebraic categories, Drexel Institute of Technology lecture notes, 1-25.Google Scholar
4. Dauns, J. and Hofmann, K. H., The representation of rings by sections, Mem. Amer. Math. Soc. 53 (1968), 1–180.Google Scholar
5. Dauns, J. and Hofmann, K. H., Spectral theory of algebras and adjunction of identity, Math. Ann. 179 (1969), 175–202.Google Scholar
6. Dauns, J., Multiplier rings and primitive ideals, Trans. Amer. Math. Soc. 145 (1969), 125–158.Google Scholar
7. Delaroche, C., Sur les centres des C*-algèbres, Bull. Sci. math. 91 (1967), 105–112.Google Scholar
8. Delaroche, C., Sur les centres des C*-algebres, II, Bull. Sci. math. 92 (1968), 111–128.Google Scholar
9. Dixmier, J., Ideal center of a C*-algebra, Duke Math. J. 35 (1968), 375–382.Google Scholar
10. Dixmier, J., Les C*-algebres et leurs représentations (Gauthier-Villars, Paris, 1969).Google Scholar
11. Rickart, C., General theory of Banach algebras (Von Nostrand, Princeton, 1960).Google Scholar