Skip to main content
SpringerLink
Log in

Hilbert \(C^*\)-Modules Related to Discrete Metric Spaces

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

It is shown that the metric on the union of the sets X and Y defines a Hilbert \(C^*\)-module over the uniform Roe algebra of the space X with a fixed metric dX. A number of examples of such Hilbert \(C^*\)-modules are described.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Paschke, W.L. "Inner product modules over \(B^*\)-algebras", Trans. Amer. Math. Soc. 182, 443-468 (1972).

    MathSciNet  MATH  Google Scholar 

  2. Frank, M. "Self-duality and \(C^*\)-reflexivity of Hilbert \(C^*\)-modules", Zeitschr. Anal. Anw. 9, 165-176 (1990).

    Article  Google Scholar 

  3. Paschke, W.L. "The double B-dual of an inner product module over a \(C^*\)-algebra B", Canad. J. Math. 26, 1272-1280 (1974).

    Article  MathSciNet  Google Scholar 

  4. Frank, M., Manuilov, V.M., Troitsky, E.V. "A reflexivity criterion for Hilbert \(C^*\)-modules over commutative \(C^*\)-algebras", New York J. Math. 16, 399-408 (2010).

    MathSciNet  MATH  Google Scholar 

  5. Manuilov, V., Troitsky, E. "Hilbert \(C^*\)-and \(W^*\)-modules and their morphisms", J. Math. Sci. 98 (2), 137-201 (2000).

    Article  MathSciNet  Google Scholar 

  6. Nowak, P.W., Guoliang, Yu. Large scale geometry (EMS Textbooks in Math. European Math. Soc., Zürich, 2012 ).

    Book  Google Scholar 

  7. Roe, J. Lectures on coarse geometry, Univ. Lect. Ser. 31 (Amer. Math. Soc., Providence, 2003 ).

    MATH  Google Scholar 

  8. Frank, M. "Hilbert \(C^*\)-modules over monotone complete \(C^*\)-algebras", Math. Nachr. 175, 61-83 (1995).

    Article  MathSciNet  Google Scholar 

  9. Manuilov, V. "Metrics on doubles as an inverse semigroup", J. Geom. Anal. 31 (2021).

  10. Exel, R. "Noncommutative Cartan subalgebras of \(C^*\)-algebras", New York, J. Math. 17, 331-382 (2011).

    MathSciNet  MATH  Google Scholar 

  11. Manuilov, V. "Roe bimodules as morphisms of discrete metric spaces", Russian J. Math. Phys. 26, 470-478 (2019).

    Article  MathSciNet  Google Scholar 

  12. Gromov, M. Geometric Group Theory, Vol. 2, London Math. Soc. Lect. Note Ser. 182 (CUP, Cambridge, 1993).

    Google Scholar 

Download references

Funding

This work is supported by the Russian Science Foundation under grant no. 21-11-00080.

Author information

Authors and Affiliations

  1. Moscow Center for Fundamental and Applied Mathematics,Moscow State University, 1 Leninskie Gory, 119991, Moscow, Russia

    V. M. Manuilov

Authors
  1. V. M. Manuilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. M. Manuilov.

Additional information

To the memory of Yuri Grigorievich Borisovich

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 55–63.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manuilov, V.M. Hilbert \(C^*\)-Modules Related to Discrete Metric Spaces. Russ Math. 65, 40–47 (2021). https://doi.org/10.3103/S1066369X21050078

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X21050078

Keywords

Search

Navigation