, Volume 14, Issue 4, pp 567–575 | Cite as

W. A. J. Luxemburg: a remarkable mathematician



This is an article describing some of the mathematical contributions of W. A. J. Luxemburg.


Banach function spaces Orlicz spaces Positive operators Non-standard analysis 

Mathematics Subject Classification (2000)

Primary 01A70 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Academic Press (1985)Google Scholar
  2. 2.
    Ellis H.W., Halperin I.: Function spaces determined by a levelling length function. Can. J. Math. 5, 576–592 (1953)MATHMathSciNetGoogle Scholar
  3. 3.
    Grothendieck A.: Réarrangements de fonctions et inégalités de convexité dans les algèbres de von Neumann munies d’une trace. Seminaire Bourbaki 113, 1–13 (1955)Google Scholar
  4. 4.
    Lorentz G.G.: Some new functional spaces. Ann. Math. 51, 37–55 (1950)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Lorentz G.G.: On the theory of the spaces Λ. Pac. J. Math. 1, 411–429 (1950)MathSciNetGoogle Scholar
  6. 6.
    Luxemburg, W. A. J.: Banach Function Spaces. Thesis, Delft (1955)Google Scholar
  7. 7.
    Luxemburg W. A. J.: Two applications of the method of construction by ultrapowers to analysis. Bull. Am. Math. Soc. 68, 416–419 (1962)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Luxemburg W. A. J., Zaanen A.C.: Compactness of integral operators in Banach function spaces. Math. Ann. 149, 150–180 (1963)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Luxemburg, W. A. J., Zaanen, A.C.: Notes on Banach function spaces. Notes I–XIII. Nederl. Akad. Wetensch. Proc. A66–A67 (1963–1964)Google Scholar
  10. 10.
    Luxemburg W.A.J.: Notes on Banach function spaces. Notes XIV–XVI. Nederl. Akad. Wetensch. Proc. Ser. A68=Indag. Math 27, 229–248 (1965) 415–446; 646–657Google Scholar
  11. 11.
    Luxemburg, W. A. J.: Non-standard analysis. Lectures on A. Robinson’s theory of infinitesimals and infinitely large numbers. Mathematics Department, Califormia Institute of Technology, Pasadena, California (1964)Google Scholar
  12. 12.
    Luxemburg, W. A. J.: Rearrangement-invariant Banach function spaces. In: Proc. Symposium in Analysis (Queen’s University, 1967). Queeen’s Papers in Pure and Appl. Math. 10, 83–144 (1967)Google Scholar
  13. 13.
    Luxemburg, W. A. J.: A general theory of monads. Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Symposium, Pasadena, Calif., 1969), pp. 18–86. Holt, Rinehart and Winston, New York (1969)Google Scholar
  14. 14.
    Luxemburg, W. A. J., Zaanen, A.C.: Riesz Spaces I, xi+514 pp. North-Holland Mathematical Library, North-Holland, Amsterdam-London; American Elsevier Publishing Co., New York (1971)Google Scholar
  15. 15.
    Luxemburg, W. A. J.: Spaces of measurable functions. In: Jeffrey-Williams Lectures 1968–1972. Canad. Math. Congr., pp. 45–71 (1972)Google Scholar
  16. 16.
    Luxemburg, W. A. J., Stroyan, K.D.: Introduction to the theory of infinitesimals. In: Pure and Applied Mathematics, No 72. Academic Press (Harcourt-Brace-Jovanovich), xiii+326 pp (1976)Google Scholar
  17. 17.
    Luxemburg, W. A. J.: The work of Dorothy Maharam on kernel representations of linear operators. In: Measure and Measurable Dynamics (Rochester, NY, 1987), pp 177–183. Am. Math. Soc., Providence (1989)Google Scholar
  18. 18.
    Meyer-Nieberg P. (1991) Banach Lattices. Universitext, Springer-VerlagGoogle Scholar
  19. 19.
    Orlicz, W.: Über eine gewisse Klasse von Räume vom typus B. Bull. Int. Acad. Polon. Sci. Lett. Cl. Math. Nat A, 207–220 (1932)Google Scholar
  20. 20.
    Riesz F.: Untersuchungen über Systeme integrierbarer Functionen. Math. Ann. 69, 449–497 (1910)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Riesz F.: Sur la décomposition des opérations fonctionelles linéaires. Atti Congr. Internaz. Mat. Bologna 3, 143–148 (1928)Google Scholar
  22. 22.
    Schaefer H.H.: Banach Lattices and Positive Operators. Springer-Verlag, Berlin, Heidelberg, New York (1974)MATHGoogle Scholar
  23. 23.
    Vulikh B.Z.: Introduction to the Theory of Partially Ordered Spaces. Wolters-Noordhoff, Groningen (1967)MATHGoogle Scholar
  24. 24.
    Zaanen, A.C.: Integration. North-Holland (1967)Google Scholar
  25. 25.
    Zaanen, A.C.: Riesz Spaces II. North-Holland (1983)Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.School of Computer Science, Mathematics and EngineeringFlinders UniversityAdelaideAustralia

Personalised recommendations