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Coarse Structure of Metrizable Hypergroups

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Abstract

In this paper, we study proper left invariant metrics of hypergroups and show that any two proper left invariant metrics on a hypergroup, are coarsely equivalent.

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References

  1. Birkhoff, G.: A note on topological groups. Compos. Math. 3, 427–430 (1936)

    MathSciNet  MATH  Google Scholar 

  2. Bloom, W.R., Heyer, H.: Harmonic Analysis of Probability Measures on Hypergroups. De Gruyter, Berlin (1995)

    Book  Google Scholar 

  3. Haagerup, U., Przybyszewska, A.: Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces, arXiv:math/0606794v1. [math.OA] (2006)

  4. Jewett, R.I.: Spaces with an abstract convolution of measures. Adv. Math. 18, 1–101 (1975)

    Article  MathSciNet  Google Scholar 

  5. Kakutani, S.: Uber die Metrisation der topologischen Gruppen. Proc. Imp. Acad. Tokyo 12, 82–84 (1936)

    MathSciNet  MATH  Google Scholar 

  6. Lubotzky, A., Mozes, S., Ragunathan, M.S.: The word and riemannian metrics on lattices of semisimple groups. Publications Mathematiques, IHES, 91 (2000)

  7. Roe, J.: Lectures on Coarse Geometry, University Lecture Series, vol. 31. American Mathematical Society, Providence (2003)

    MATH  Google Scholar 

  8. Rosendal, C.: Coarse Geometry of Topological Groups. Cambridge University Press, Cambridge (2021)

    Book  Google Scholar 

  9. Struble, R.A.: Metrics in locally compact groups. Compositio Mathematica. 28, 217–222 (1974)

    MathSciNet  MATH  Google Scholar 

  10. Tabatabaie, S.M., Amini, M.: Convolution coarse structures. Topol. Appl. 275, 107152 (2020). https://doi.org/10.1016/j.topol.2020.107152

    Article  MathSciNet  MATH  Google Scholar 

  11. Tu, J.L.: Remarks on Yu’s “Property A” for discrete metric spaces and groups. Bull. Soc. Math. France 1(129), 115–139 (2001)

  12. Voit, M.: Hypergroup with invariant metrics. Am. Math. Soc. 126(9), 2635–2640 (1998)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

    Massoud Amini

  2. Department of Mathematics, University of Qom, Qom, Iran

    Ali Asghar Amjadi & Seyyed Mohammad Tabatabaie

Authors
  1. Massoud Amini
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  2. Ali Asghar Amjadi
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  3. Seyyed Mohammad Tabatabaie
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Corresponding author

Correspondence to Seyyed Mohammad Tabatabaie.

Additional information

Communicated by Daniel Alpay.

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This article is part of the topical collection “Infinite-dimensional Analysis and Non-commutative Theory” edited by Marek Bozejko, Palle Jorgensen and Yuri Kondratiev.

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Amini, M., Amjadi, A.A. & Tabatabaie, S.M. Coarse Structure of Metrizable Hypergroups. Complex Anal. Oper. Theory 16, 9 (2022). https://doi.org/10.1007/s11785-021-01191-7

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  • DOI: https://doi.org/10.1007/s11785-021-01191-7

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