Ideal Structure of Some C*-algebras

Document Type : Original Paper

Authors

1 Department of Mathematics, Statistics and Computer Sciences, College of Sciences, University of Tehran, Tehran, Iran

2 Department of mathematics, statistics and computer science,, Faculty of Science,, University of Tehran.,

Abstract

In this note, considering the main properties of closed ideals of C*-algebras, we will determine the structure of closed ideals of the C*-algebra C(X, A), the space of all continuous functions from compact Hausdorff space X to C*_algebra A. Indeed, we will show that for every closed ideal of C(X, A), there is some closed subset F of topological space X × prim(A), such that {f ∈ C(X, A) : ∀ (x, P )∈F , f(x) ∈ P}=I.

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References

[1] Aupetit, B., 1991. A primer on spectral theory, Springer­Verlag, New York. doi:101007/978­1­4612­
3048­9
[2] Blackadar, B., 2006. Operator algebras. Theory of C*­algebras and von Neumann algebras, Encyclopaedia of Mathematical Sciences, vol. 122: Operator Algebras and Non­commutative Geometry,
III, Springer­Verlag, Berlin.
[3] Blanchard, E. and Kircher, E., 2004. Non­simple purely infinite C*­algebras: the Hausdorff case, J.
Funct. Anal., 207, pp.461­513. doi:10.1016/j.jfa.2003.06.008
[4] Conway, J.B., 1999. A course in operator theory, Amer. Math. Soci. doi: 10.1090/gsm/021
[5] Murphy, G. J., 1990. C*­algebras and operator theory, Academic Press Inc., Boston, MA,

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History

  • Receive Date: 18 June 2023
  • Revise Date: 13 October 2023
  • Accept Date: 10 April 2024

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