Hypergroups with invariant metric
HTML articles powered by AMS MathViewer
- by Michael Voit PDF
- Proc. Amer. Math. Soc. 126 (1998), 2635-2640 Request permission
Abstract:
The purpose of this note is to extend the following classical result from groups to hypergroups in the sense of C.F. Dunkl, R.I. Jewett, and R. Spector: If a hypergroup has a countable neighborhood base of its identity, then $K$ admits a left- or a right-invariant metric. Moreover, it admits an invariant metric if and only if there exists a countable conjugation-invariant neighborhood base of the identity.References
- G. Birkhoff: A note on topological groups. Compos. Math. 3, 427 – 430 (1936).
- Walter R. Bloom and Herbert Heyer, Harmonic analysis of probability measures on hypergroups, De Gruyter Studies in Mathematics, vol. 20, Walter de Gruyter & Co., Berlin, 1995. MR 1312826, DOI 10.1515/9783110877595
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Robert I. Jewett, Spaces with an abstract convolution of measures, Advances in Math. 18 (1975), no. 1, 1–101. MR 394034, DOI 10.1016/0001-8708(75)90002-X
- S. Kakutani: Über die Metrisation der topologischen Gruppen. Proc. Imp. Acad. Tokyo 12, 82 – 84 (1936).
- Hansmartin Zeuner, One-dimensional hypergroups, Adv. Math. 76 (1989), no. 1, 1–18. MR 1004484, DOI 10.1016/0001-8708(89)90041-8
Additional Information
- Michael Voit
- Affiliation: Mathematisches Institut, Universität Tübingen, 72076 Tübingen, Germany; Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, Virginia 22903-3199
- MR Author ID: 253279
- ORCID: 0000-0003-3561-2712
- Email: voit@uni-tuebingen.de
- Received by editor(s): December 26, 1996
- Received by editor(s) in revised form: January 27, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2635-2640
- MSC (1991): Primary 43A62; Secondary 20N20, 54E35
- DOI: https://doi.org/10.1090/S0002-9939-98-04366-4
- MathSciNet review: 1451835