Geodesic
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 415-422

Voir la notice de l'article provenant de la source Cambridge University Press

In this paperwe present a fixed point property for amenable hypergroups that is analogous to Rickert’s fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, certain hypergroups are shown to have a left Haar measure.
DOI : 10.4153/CMB-2014-069-3
Mots-clés : 43A62, 43A05, 43A07, invariant measure, Haar measure, hypergroup, amenability, function translations 
Willson, Benjamin. A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 415-422. doi: 10.4153/CMB-2014-069-3
@article{10_4153_CMB_2014_069_3,
     author = {Willson, Benjamin},
     title = {A {Fixed} {Point} {Theorem} and the {Existence} of a {Haar} {Measure} for {Hypergroups} {Satisfying} {Conditions} {Related} to {Amenability}},
     journal = {Canadian mathematical bulletin},
     pages = {415--422},
     year = {2015},
     volume = {58},
     number = {2},
     doi = {10.4153/CMB-2014-069-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-069-3/}
}
TY  - JOUR
AU  - Willson, Benjamin
TI  - A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability
JO  - Canadian mathematical bulletin
PY  - 2015
SP  - 415
EP  - 422
VL  - 58
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-069-3/
DO  - 10.4153/CMB-2014-069-3
ID  - 10_4153_CMB_2014_069_3
ER  - 
%0 Journal Article
%A Willson, Benjamin
%T A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability
%J Canadian mathematical bulletin
%D 2015
%P 415-422
%V 58
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-069-3/
%R 10.4153/CMB-2014-069-3
%F 10_4153_CMB_2014_069_3

[1] [1] Alaghmandan, M., Amenability notions of hypergroups and some applications to locally compact groups. arxiv:1 402.2263 Google Scholar

[2] [2] Bloom, W. R. and Heyer, H., Harmonie analysis of probability measures on hypergroups. de Gruyter Studies in Mathematics, 20, Walter de Gruyter & Co., Berlin, 1995. Google Scholar

[3] [3] Dunkl, C. F., The measure algebra of a locally compact hypergroup. Trans. Amer. Math. Soc. 179 (1973), 331–348. http://dx.doi.Org/10.1090/S0002–9947-1973-0320635-2 Google Scholar

[4] [4] Hewitt, E. and Ross, K. A., Abstract harmonic analysis. Vol. I. Structure of topological groups, integration theory, group representations. Grundlehren der Mathematischen Wissenschaften, 115, Springer-Verlag, Berlin-New York, 1979. Google Scholar

[5] [5] Izzo, A. J., A functional analysis proof of the existence ofHaar measure on locally compact abelian groups. Proc. Amer. Math. Soc. 115 (1992), no. 2, 581–583. http://dx.doi.Org/10.1090/S0002-9939-1992-1097346-9 Google Scholar

[6] [6] Jewett, R. I., Spaces with an abstract convolution of measures. Advances in Math. 18 (1975), no. 1, 1–101. http://dx.doi.Org/10.1016/0001-8708(75)90002-X Google Scholar

[7] [7] Lasser, R. and Skantharajah, M., Reiter's condition for amenable hypergroups, Monatsh Math 63 (2010), no. 3, 327–338. http://dx.doi.Org/10.1007/s00605-010-0206-z Google Scholar

[8] [8] Paterson, A. L. T., Amenability. Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, RI, 1988. Google Scholar

[9] [9] Rosenblatt, J. M., Invariant measures and growth conditions. Trans. Amer. Math. Soc. 193 (1974), 33–53. http://dx.doi.Org/10.1090/S0002-9947-1974-0342955-9 Google Scholar

[10] [10] Singh, A. I., Completely positive hypergroup actions. Mem. Amer. Math. Soc. 124 (1996), no 593. Google Scholar

[11] [11] Skantharajah, M., Amenable hypergroups. Illinois J. Math. 36 (1992), no. 1,15–46. Google Scholar

[12] [12] Spector, R., Mesures invariantes sur les hypergroupes. Trans. Amer. Math. Soc. 239 (1978), 147–165. http://dx.doi.Org/10.1090/S0002–9947-1978-0463806-1 Google Scholar

[13] [13] Tahmasebi, N., Hypergroups and invariant complemented subspaces. J. Math. Anal. Appl. 414 (2014), no. 2, 641–655. http://dx.doi.Org/10.1016/j.jmaa.2014.01.026 Google Scholar

[14] [14] Willson, B., Configurations and invariant nets for amenable hypergroups and related algebras. Trans. Amer. Math. Soc. 366 (2014), no. 10, 5087–5112. Google Scholar | DOI

Cité par Sources :