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2013 | 11 | 11 | 2034-2043
Tytuł artykułu

Real-linear isometries between certain subspaces of continuous functions

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Języki publikacji
EN
Abstrakty
EN
In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
2034-2043
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
Twórcy
Bibliografia
  • [1] Araujo J., Font J.J., Linear isometries between subspaces of continuous functions, Trans. Amer. Math. Soc., 1997, 349(1), 413–428 http://dx.doi.org/10.1090/S0002-9947-97-01713-3
  • [2] Browder A., Introduction to Function Algebras, W.A. Benjamin, New York-Amsterdam, 1969
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  • [4] Dunford N., Schwartz J.T., Linear Operators I, Pure Appl. Math., 7, Interscience, New York, 1958
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  • [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] Holsztynski W., Continuous mappings induced by isometries of spaces of continuous functions, Studia Math., 1966, 26, 133–136
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  • [10] 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
  • [11] 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
  • [12] Novinger W.P., Linear isometries of subspaces of spaces of continuous functions, Studia Math., 1975, 53(3), 273–276
  • [13] Phelps R.R., Lectures on Choquet’s Theorem, 2nd ed., Lecture Notes in Math., 1757, Springer, Berlin, 2001 http://dx.doi.org/10.1007/b76887
  • [14] Roy A.K., Extreme points and linear isometries of the Banach spaces of Lipschitz functions, Canad. J. Math., 1968, 20, 1150–1164 http://dx.doi.org/10.4153/CJM-1968-109-9
  • [15] 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
  • [16] Vasavada M.H., Closed Ideals and Linear Isometries of Certain Function Spaces, PhD thesis, University of Wisconsin, Madison, 1969
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0303-z
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