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A note on disjointness preserving operators

Author: B. de Pagter
Journal: Proc. Amer. Math. Soc. 90 (1984), 543-549
MSC: Primary 47B55; Secondary 46A40
MathSciNet review: 733403
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Abstract: In this paper we present some results concerning the automatic order boundedness of disjointness preserving operators on Riesz spaces (vector lattices).

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  • Yuri A. Abramovich, Multiplicative representation of disjointness preserving operators, Nederl. Akad. Wetensch. Indag. Math. 45 (1983), no. 3, 265–279. MR 718068
  • Yu. A. Abramovich, A. I. Veksler and A. V. Koldunov, On operators preserving disjointness, Soviet Math. Dokl. 20 (1979), 1089-1093. ---, Operators preserving disjointness, their continuity and multiplicative representation, Linear Operators and Their Applications, Leningrad, 1981, pp. 13-34. (Russian)
  • Charalambos D. Aliprantis and Owen Burkinshaw, Locally solid Riesz spaces, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics, Vol. 76. MR 0493242
  • Wolfgang Arendt, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), no. 2, 199–215. MR 690185, DOI
  • S. J. Bernau, Orthomorphisms of archimdean vector lattices, Tech. Rep. 14, Univ. of Texas, Austin, 1979.
  • Alain Bigard, Klaus Keimel, and Samuel Wolfenstein, Groupes et anneaux réticulés, Lecture Notes in Mathematics, Vol. 608, Springer-Verlag, Berlin-New York, 1977 (French). MR 0552653
  • W. A. J. Luxemburg, Some aspects of the theory of Riesz spaces, University of Arkansas Lecture Notes in Mathematics, vol. 4, University of Arkansas, Fayetteville, Ark., 1979. MR 568706
  • W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam and London, 1971.
  • Mathieu Meyer, Le stabilisateur d’un espace vectoriel réticulé, C. R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 5, Aii, A249–A250. MR 433191
  • ---, Quelques propriétés des homomorphismes d’espaces vectoriels réticulés, Equipe d’Analyse, E.R.A. 294, Université de Paris VI, 1979. B. de Pagter, $f$-algebras and orthomorphisms, Thesis, University of Leiden, 1981.
  • A. W. Wickstead, Extensions of orthomorphisms, J. Austral. Math. Soc. Ser. A 29 (1980), no. 1, 87–98. MR 566279
  • A. C. Zaanen, Examples of orthomorphisms, J. Approximation Theory 13 (1975), 192–204. MR 355527, DOI

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Keywords: Disjointness preserving operator, automatic order boundedness, orthomorphism
Article copyright: © Copyright 1984 American Mathematical Society