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Algebraic reflexivity of diameter-preserving linear bijections between C(X)-spaces

  • Jim´enez-Vargas, Antonio [2] ; Sady, Fereshteh [1]
    1. [1] Tarbiat Modares University

      Tarbiat Modares University

      Irán

    2. [2] Universidad de Almer´ıa. Departamento de Matem´aticas
  • Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 2, 2021, págs. 727-746
  • Idioma: inglés
  • DOI: 10.5565/publmat6522110
  • Enlaces
  • Resumen
    • We prove that if X and Y are first countable compact Hausdorff spaces, then the set of all diameter-preserving linear bijections from C(X) to C(Y ) is algebraically reflexive.

  • Referencias bibliográficas
    • A. Aizpuru and F. Rambla, There’s something about the diameter, J. Math. Anal. Appl. 330(2) (2007), 949–962. DOI: 10.1016/j.jmaa.2006.08.002.
    • B. A. Barnes and A. K. Roy, Diameter-preserving maps on various classes of function spaces, Studia Math. 153(2) (2002), 127–145. DOI: 10.4064/sm153-2-3.
    • F. Botelho and J. Jamison, Algebraic and topological reflexivity of spaces of Lipschitz functions, Rev. Roumaine Math. Pures Appl. 56(2) (2011),...
    • F. Cabello Sanchez , Diameter preserving linear maps and isometries, Arch. Math. (Basel) 73(5) (1999), 373–379. DOI: 10.1007/s000130050411.
    • F. Cabello Sanchez and L. Molnar , Reflexivity of the isometry group of some classical spaces, Rev. Mat. Iberoamericana 18(2) (2002), 409–430....
    • S. Dutta and T. S. S. R. K. Rao, Algebraic reflexivity of some subsets of the isometry group, Linear Algebra Appl. 429(7) (2008), 1522–1527....
    • J. J. Font and M. Hosseini, Nonlinear diameter preserving maps on function spaces, Quaest. Math. 43(1) (2020), 67–80. DOI: 10.2989/16073606.2018....
    • A. M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171–172. DOI: 10.1007/BF02788714.
    • F. Gonzalez and V. V. Uspenskij , On homomorphisms of groups of integervalued functions, Extracta Math. 14(1) (1999), 19–29.
    • M. Gyory, Diameter preserving linear bijections of C0(X), Publ. Math. Debrecen 54(1–2) (1999), 207–215.
    • M. Gyory and L. Molnar , Diameter preserving linear bijections of C(X), Arch. Math. (Basel) 71(4) (1998), 301–310. DOI: 10.1007/s000130050268.
    • W. Holsztynski , Continuous mappings induced by isometries of spaces of continuous functions, Studia Math. 26 (1966), 133–136. DOI: 10.4064/sm-26-2-133...
    • A. Jamshidi and F. Sady, Nonlinear diameter preserving maps between certain function spaces, Mediterr. J. Math. 13(6) (2016), 4237–4251. DOI:...
    • K. Jarosz and T. S. S. R. K. Rao, Local isometries of function spaces, Math. Z. 243(3) (2003), 449–469. DOI: 10.1007/s00209-002-0452-4.
    • A. Jimenez-Vargas, A. Morales Campoy, and M. Villegas-Vallecillos , Algebraic reflexivity of the isometry group of some spaces of Lipschitz...
    • J.-P. Kahane and W. Zelazko , A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339–343. DOI: 10.4064/...
    • L. Li, A. M. Peralta, L. Wang, and Y.-S. Wang, Weak-2-local isometries on uniform algebras and Lipschitz algebras, Publ. Mat. 63(1) (2019),...
    • L. Molnar and B. Zalar ´ , Reflexivity of the group of surjective isometries on some Banach spaces, Proc. Edinburgh Math. Soc. (2) 42(1) (1999),...
    • S. Oi, Algebraic reflexivity of isometry groups of algebras of Lipschitz maps, Linear Algebra Appl. 566 (2019), 167–182. DOI: 10.1016/j.laa.2018.12.033.
    • T. S. S. R. K. Rao and A. K. Roy, Diameter-preserving linear bijections of function spaces, J. Aust. Math. Soc. 70(3) (2001), 323–335. DOI:...
    • W. Zelazko , A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83–85. DOI: 10.4064/sm-30-1-83-85.

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