Inner amenable hypergroups, invariant projections and Hahn-Banach extension theorem related to hypergroups

Authors

  • Nazanin TAHMASEBI Department of Mathematical and Statistical Sciences, University of Alberta, AB, Canada, Department of Computing Sciences, University of Alberta, AB, Canada, Servier Virtual Cardiac Centre, Mazankowski Alberta Heart Institute, AB, Canada e-mail: ntahmase@ualberta.ca https://orcid.org/0000-0002-6461-578X

Abstract

Let K be a hypergroup with a Haar measure. In the present paper we initiate the study of inner amenable hypergroups extending amenable hy pergroups and inner amenable locally compact groups. We also provide charac terizations of amenable hypergroups by hypergroups having the Hahn-Banach extension or monotone projection property. Finally we focus on weak*-invariant complemented subspaces of L1(K).

Mathematics Subject Classification (2010): 43A07.

References

Bloom, W., Heyer, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, 20, Berlin, 1995.

Chapovsky, Y., Vainerman, L.I., Compact quantum hypergroups, J. Operator Theory, 41(1999), no. 2, 261-289.

Choda, H., Choda, M., Fullness, simplicity and inner amenability, Math. Japon., 24(1979), no. 2, 235-246.

Choda, M., Effect of inner amenability on strong ergodicity, Math. Japon., 28(1983), no. 1, 109-115.

Dunkl, C.F., Ramirez, D.E., A family of countably compact P-hypergroups, Trans. Amer. Math. Soc., 202(1975), 339-356.

Dunkl, C.F., The measure algebra of a locally compact hypergroup, Trans. Amer. Hath. Soc., 179(1973), 331-348.

Eros, E.G., Property and inner amenability, Proc. Amer. Math. Soc., 47(1975), 483-486.

Ghahramani, F., Medgalchi, A.R., Compact multipliers on weighted hypergroup algebras, Math. Proc. Cambridge Philos. Soc., 98(1985), no. 3, 493-500.

Ghahramani, F., Medgalchi, A.R., Compact multipliers on weighted hypergroup algebras. II, Math. Proc. Cambridge Philos. Soc., 100(1986), no. 1, 145-149.

Grosser, M., Arens semiregular Banach algebras, Monatsh. Math., 98(1984), no. 1, 41-52.

Hermann, P., Induced representations and hypergroup homomorphisms, Monatsh. Math., 116(1993), 245-262.

Jewett, R.I., Spaces with an abstract convolution of measures, Advances in Math., 18(1975), 1-101.

Lasser, R., Amenability and weak amenability of l1-algebras of polynomial hypergroups, Studia Math., 182(2007), no. 2, 183-196.

Lasser, R., Orthogonal polynomials and hypergroups. II. The symmetric case, Trans. Amer. Math. Soc., 341(1994), no. 2, 749-770.

Lasser, R., Skantharajah, M., Reiter's condition for amenable hypergroups, Monatsh. Math., 163(2011), no. 3, 327-338.

Lau, A. T.-M., Amenability and invariant subspaces, J. Austral. Math. Soc., 18(1974), no. 2, 200-204.

Lau, A. T.-M., Paterson, A.L.T., Inner amenable locally compact groups, Trans. Amer. Math. Soc., 325(1991), no. 1, 155-169.

Lau, A. T.-M., Invariantly complemented subspaces of L1(G) and amenable locally compact groups, Illinois J. Math., 26(1982), 226-235.

Lau, A. T.-M., Paterson, A.L.T., Operator theoretic characterizations of [IN]-groups and inner amenability, Proc. Amer. Math. Soc., 102(1988), no. 4, 893-897.

Lau, A. T.-M., Operators which commute with convolutions on subspaces of L1(G), Colloq. Math., 39(1978), no. 2, 351-359.

Losert, V., Rindler, H., Asymptotically central functions and invariant extensions of Dirac measure, Probability measures on groups, VII, Oberwolfach, 1983, 368-378.

Losert, V., Rindler, H., Conjugation-invariant means, Colloq. Math., 51(1987), 221-225.

Mitchell, T., Function algebras, means, and fixed points, Trans. Amer. Math. Soc., 130(1968), 117-126.

Ross, K.A., Centers of hypergroups, Trans. Amer. Math. Soc., 243(1978), 251-269.

Ross, K.A., LCA hypergroups, Topology Proc., 24(1999), 533-546.

Ross, K.A., Hypergroups and centers of measure algebras, Symposia Mathematica, XXII(1997), 189-203.

Sinclair, A.M., Continuous semigroups in Banach algebras, London Mathematical Society Lecture Note Series, 63, Cambridge University Press, Cambridge-New York, 1982.

Skantharajah, M., Amenable hypergroups, Illinois J. Math., 36(1992), no. 1, 15-46.

Spector, R., Apercu de la theorie des hypergroupes, Lecture Notes in Math., Vol. 497, Springer, Berlin, 1975, 643-673.

Stokke, R., Quasi-central bounded approximate identities in group algebras of locally compact groups, Illinois J. Math., 48(2004), no. 1, 151-170.

Tahmasebi, N., Hypergroups and invariant complemented subspaces, J. Math. Anal. Appl., 414(2014), 641-655.

Tahmasebi, N., Fixed point properties, invariant means and invariant projections related to hypergroups, J. Math. Anal. Appl., 437(2016), 526-544.

Voit, M., Duals of subhypergroups and quotients of commutative hypergroups, Math. Z., 210(1992), no. 2, 289-304.

Willson, B., Configuration and invariant nets for amenable hypergroups and related algebras, Trans. Amer. Math. Soc., 366(2014), no. 10, 5087-5112.

Zeuner, H., Duality of commutative hypergroups, Probability measures on groups, Oberwolfach, 10(1990), 467-488.

Zeuner, H., Moment functions and laws of large numbers on hypergroups, Math. Z., 211(1992), no. 3, 369-407.

STUDIA UBB MATHEMATICA, Volume 61 (LXI), No. 2, June 2016

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2016-06-30

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TAHMASEBI, N. (2016). Inner amenable hypergroups, invariant projections and Hahn-Banach extension theorem related to hypergroups. Studia Universitatis Babeș-Bolyai Mathematica, 61(2), 195–220. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5553

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Volume 61, No. 2, June 2016

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