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Exhaustivity in topologicai Riesz spaces with the principal projection property

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Exhaustive and uniformly exhaustive elements are studied in the setting of locally solid topological Riesz spaces with the principal projection property. We study the structure of the order interval [O, χ] when x is an exhaustive element and the structure of the solid hull of a set of uniformly exhaustive elements.
Rocznik
Strony
53--62
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • Department of Mathematics, Lake Superior State University, Sault Sainte Marie, MI 49783, U.S.A., kmuller@lssu.edu
Bibliografia
  • [1] C. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces, Academic Press, New York, 1978.
  • [2] —, —, Positive Operators, Academic Press, New York, 1985.
  • [3] W. Bell, R. Bilyeu and P. Lewis, Uniform exhaustivity and Banach lattices, Ann. Mat. Pura Appl. 4 (1944), 57-74.
  • [4] R. Bilyeu and P. Lewis, Uniform differentiability, uniform absolute continuity, and the Vitali-Hahn Saks theorem, Rocky Mountain J. Math. 10 (1980), 533-557.
  • [5] J. Brooks, Equicontinuous sets of measures and applications to Vitali 's integral convergence theorem and control measures, Ad. Math. 10 (1973), 165-171.
  • [6] J. Brooks and R. Jewett, On finitely additive vector measures, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 1294-1298.
  • [7] J. Brooks and P. Lewis, Linear operators and vector measures, Trans. Amer. Math. Soc. 192 (1974), 139-162.
  • [8] J. Diestel and B. Faires, On vector measures, ibid. 198 (1974), 253-271.
  • [9] J. Diestel and J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
  • [10] L. Drewnowski, Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym theorems, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 725-731.
  • [11] —, Topological rings of sets, continuous set functions, integration. II, ibid. 80 (1972), 277-286.
  • [12] L. Drewnowski and I. Labuda, Copies of Co and l∞ in topological Riesz spaces, Trans. Amer. Math. Soc. 350 (1998), 3555-3570.
  • [13] C. Huff and P. Lewis, Exhaustive submeasures on boolean rings, Banach lattices, and uniform absolute continuity. Bull. Polish Acad. Sci. Math. 49 (2001), 203-210.
  • [14] S. Kakutani, Concrete representation of abstract (L)-spaces, Ann. of Math. 42 (1941), 523-537.
  • [15] —, Notes on infinite product measure spaces II, Proc. Imp. Acad. Tokyo 19 (1943), 184-188.
  • [16] P. Lewis and K. Muller, Isomorphic embeddings and strongly additive measures, Monatsh. Math. 143 (2004), 21-33.
  • [17] W. Luxemburg and A. Zaanen, Riesz Spaces, Vol. 1, North-Holland, Amsterdam, 1971.
  • [18] P. Meyer-Nieberg, Zur schwachen Kompaktheit in Banachverbänden, Math. Z. 134 (1973), 303-315.
  • [19] H. Schaefer, Banach Lattices and Positive Operators, Springer, New York, 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0011-0014
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