A note on disjointness preserving operators
HTML articles powered by AMS MathViewer
- by B. de Pagter PDF
- Proc. Amer. Math. Soc. 90 (1984), 543-549 Request permission
Abstract:
In this paper we present some results concerning the automatic order boundedness of disjointness preserving operators on Riesz spaces (vector lattices).References
- Yuri A. Abramovich, Multiplicative representation of disjointness preserving operators, Nederl. Akad. Wetensch. Indag. Math. 45 (1983), no. 3, 265–279. MR 718068, DOI 10.1016/1385-7258(83)90062-8 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, Pure and Applied Mathematics, Vol. 76, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0493242
- Wolfgang Arendt, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), no. 2, 199–215. MR 690185, DOI 10.1512/iumj.1983.32.32018 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, DOI 10.1007/BFb0067004
- 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, DOI 10.1017/S1446788700020966
- A. C. Zaanen, Examples of orthomorphisms, J. Approximation Theory 13 (1975), 192–204. MR 355527, DOI 10.1016/0021-9045(75)90052-0
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 543-549
- MSC: Primary 47B55; Secondary 46A40
- DOI: https://doi.org/10.1090/S0002-9939-1984-0733403-7
- MathSciNet review: 733403