Skip to main content
Log in

The Gelfand-Naimark theorem for C*-algebras over a ring of measurable functions

  • Published:
Russian Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. I. Kaplansky, “Modules Over Operator Algebras,” Amer. J. Math. 75(4), 839–858 (1953).

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Takeuti, “C*-Algebras and Boolean Valued Analysis,” Japan J. Math. 9(2), 207–246 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. G. Kusraev, Vector Duality and Its Applications (Nauka, Novosibirsk, 1985) [in Russian].

    MATH  Google Scholar 

  4. A. G. Kusraev, Boolean Valued Analysis of Involutive Banach Algebras (North Ossetian State University, Vladikavkaz, 1996) [in Russian].

    Google Scholar 

  5. A. G. Kusraev, Majorized Operators (Nauka, Moscow, 2003) [in Russian].

    Google Scholar 

  6. A. E. Gutman, “Banach Bundles in the Theory of Lattice-Normalized Spaces,” in Linear Operators Coordinated with the Order (Russian Academy of Science, Siberian Branch, Institute of Mathematics), 29, 63–211 (1995).

    MATH  Google Scholar 

  7. I. G. Ganiev and V. I. Chilin, “Measurable Bundles of C*-Algebras,” Vladikavk. Matem. Zhurn, 5(1), 35–38 (2003).

    MathSciNet  MATH  Google Scholar 

  8. O. Bratteli and D. Robinson, Operator Algebras and Quantum Statical Mechanics. 1. C*-and W*-Algebras, Symmetry Groups, Decomposition of States (Springer-Verlag, New York, 1979; Mir, Moscow, 1982).

    Book  MATH  Google Scholar 

  9. I. G. Ganiev and K. K. Kudaibergenov, “Finite-Dimensional Modules over a Ring of Measurable Functions,” Uzb. Matem. Zhurn, No. 4, 3–9 (2004).

  10. N.M. Abasov and A. G. Kusraev, “Cyclic Compactification and the Space of Continuous Vector Functions,” Sib. Matem. Zhurn, 28(1), 17–22 (1987).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Chilin.

Additional information

Original Russian Text © V.I. Chilin, I.G. Ganiev, K.K. Kudaibergenov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 2, pp. 60–68

About this article

Cite this article

Chilin, V.I., Ganiev, I.G. & Kudaibergenov, K.K. The Gelfand-Naimark theorem for C*-algebras over a ring of measurable functions. Russ Math. 52, 58–66 (2008). https://doi.org/10.3103/S1066369X08020096

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X08020096

Keywords

Navigation