Real linear isometries between function algebras. II

Osamu Hatori 1  and Takeshi Miura
  • 1 Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
  • 2 Department of Applied Mathematics and Physics, Graduate School of Science and Engineering, Yamagata University, Yonezawa, 992-8510, Japan

Abstract

We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

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  • [1] Ellis A.J., Real characterizations of function algebras amongst function spaces, Bull. London Math. Soc., 1990, 22(4), 381–385 http://dx.doi.org/10.1112/blms/22.4.381

  • [2] Fleming R.J., Jamison J.E., Isometries on Banach Spaces: Function Spaces, Chapman Hall/CRC Monogr. Surv. Pure Appl. Math., 129, Chapman&Hall/CRC, Boca Raton, 2003

  • [3] de Leeuw K., Rudin W., Wermer J., The isometries of some function spaces, Proc. Amer. Math. Soc., 1960, 11(5), 694–698 http://dx.doi.org/10.1090/S0002-9939-1960-0121646-9

  • [4] Miura T., Real-linear isometries between function algebras, Cent. Eur. J. Math., 2011, 9(4), 778–788 http://dx.doi.org/10.2478/s11533-011-0044-9

  • [5] Nagasawa M., Isomorphisms between commutative Banach algebras with an application to rings of analytic functions, Kōdai Math. Sem. Rep., 1959, 11(4), 182–188 http://dx.doi.org/10.2996/kmj/1138844205

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