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Isomorphisms of hypergroups

  • Walter R. Bloom (a1) and Martin E. Walter (a2)

Abstract

Let K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.

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Copyright

References

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Arendt, Wolfgang and de Cannière, Jean, ‘Order isomorphisms of Fourier algebras’, J. Funct. Anal. 50 (1983), 17.
Bloom, Walter R., ‘Idempotent measures on commutative hypergroups’, Probability Measures on Groups VIII (Proc. Conf., Oberwolfach Math. Res. Inst., Oberwolfach, 1985), Lecture Notes in Math. 1210, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo 1986, 1323.
Bloom, Walter R. and Heyer, Herbert, ‘Convergence of convolution products of probability measures on hypergroups’, Rend. Mat. Ser. VII 3(1982), 547563.
Bloom, Walter R. and Heyer, Herbert, ‘Characterisation of potential kernels of transient convolution semigroups on a commutative hypergroup’, Probability Measures on Groups IX (Proc. Conf., Oberwolfach Math. Res. Inst., Oberwolfach 1988), Lecture Notes in Math. 1379, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989, pp. 2135.
Dunford, Nelson and Schwartz, Jacob T., Linear Operators, Part 1: General Theory, Interscience Publishers, New York, London, 1958.
Dunkl, Charles F., ‘The measure algebra of a locally compact hypergroup’, Trans. Amer. Math. Soc. 179 (1973), 331348.
Granirer, E. E. and Leinert, M., ‘On some topologies which coincide on the unit sphere of the Fourier-Stieltjes algebra B(G) and of the measure algebra M(G),’ Rocky Mountain J. Math. 11 (1981), 459472.
Jewett, Robert I., ‘Spaces with an abstract convolution of measures’, Adv. in Math. 18 (1975), 1101.
Johnson, B. E., ‘Isometric isomorphisms of measure algebras’, Proc. Amer. Math. Soc. 15 (1964), 186188.
Kawada, Yukiyosi, ‘On the group ring of a topological group’, Math. Jap. 1 (1948), 15.
Ross, Kenneth A., ‘Hypergroups and centers of measure algebras’, Symp. Math. 22 (1977), 189203.
Spector, R., ‘Aperçu de la théorie des hypergroupes’, Analyse Harmonique sur les Groupes de Lie (Séminaire Nancy-Strasbourg, 19731975), Lecture Notes in Math. 497, Springer-Verlag, Berlin, Heidelberg, New York, 1975, 643673.
Spector, R., ‘Mesures invariantes sur les hypergroupes’, Trans. Amer. Math. Soc. 239 (1978), 147165.
Strichartz, Robert S., ‘Isometric isomorphisms of measure algebras,’ Pacific J. Math. 15 (1965), 315317.
Walter, Martin E., ‘W*-algebras and nonabelian harmonic analysis,’ J. Funct. Acal. 11 (1972), 1738.
Wendel, J. G., ‘On isometric isomorphisms of group algebras’, J. Math. 1 (1951), 305311.
Wendel, J. G., ‘Left centralizers and isomorphisms of group algebras’, Pacific J. Math. 2 (1952), 251261.
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Isomorphisms of hypergroups

  • Walter R. Bloom (a1) and Martin E. Walter (a2)

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