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2011 | 9 | 4 | 778-788
Tytuł artykułu

Real-linear isometries between function algebras

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Języki publikacji
EN
Abstrakty
EN
Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and $T\left( f \right) = \kappa \overline {fo\phi }$ on ChB \ K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
4
Strony
778-788
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Twórcy
Bibliografia
  • [1] Araujo J., Font J.J., On Šilov boundaries for subspaces of continuous functions, Topology Appl., 1997, 77(2), 79–85 http://dx.doi.org/10.1016/S0166-8641(96)00132-0
  • [2] Burckel R.B., Characterizations of C(X) among its Subalgebras, Lecture Notes in Pure and Appl. Math., 6, Marcel Dekker, New York, 1972
  • [3] Ellis A.J., Real characterizations of function algebras amongst function spaces, Bull. Lond. Math. Soc., 1990, 22(4), 381–385 http://dx.doi.org/10.1112/blms/22.4.381
  • [4] 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
  • [5] Fleming R.J., Jamison J.E., Isometries on Banach Spaces. Vol. 2: Vector-Valued Function Spaces, Chapman Hall/CRC Monogr. Surv. Pure Appl. Math., 138, Chapman & Hall/CRC, Boca Raton, 2008
  • [6] Hatori O., Hirasawa G., Miura T., Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras, Cent. Eur. J. Math., 2010, 8(3), 597–601 http://dx.doi.org/10.2478/s11533-010-0025-4
  • [7] Hatori O., Lambert S., Luttman A., Miura T., Tonev T., Yates R., Spectral preservers in commutative Banach algebras, In: Function Spaces in Modern Analysis, Contemp. Math., 547, American Mathematical Society, Providence (in press)
  • [8] de Leeuw K., Rudin W., Wermer J., The isometries of some function spaces, Proc. Amer. Math. Soc., 1960, 11(5), 694–698
  • [9] Mazur S., Ulam S., Sur les transformations isométriques d’espaces vectoriels normés, C. R. Acad. Sci. Paris, 1932, 194, 946–948
  • [10] 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
  • [11] Rao N.V., Roy A.K., Multiplicatively spectrum-preserving maps of function algebras. II, Proc. Edinb. Math. Soc., 2005, 48(1), 219–229 http://dx.doi.org/10.1017/S0013091504000719
  • [12] Rao N.V., Tonev T.V., Toneva E.T., Uniform algebra isomorphisms and peripheral spectra, In: Topological Algebras and Applications, Contemp. Math., 427, American Mathematical Society, Providence, 2007, 401–416
  • [13] Tonev T., Toneva E., Composition operators between subsets of function algebras, In: Function Spaces in Modern Analysis, Contemp. Math., 547, American Mathematical Society, Providence (in press)
  • [14] Tonev T., Yates R., Norm-linear and norm-additive operators between uniform algebras, J. Math. Anal. Appl., 2009, 357(1), 45–53 http://dx.doi.org/10.1016/j.jmaa.2009.03.039
  • [15] Väisälä J., A proof of the Mazur-Ulam theorem, Amer. Math. Monthly, 2003, 110(7), 633–635 http://dx.doi.org/10.2307/3647749
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0044-9
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