Wilhelmus Luxemburg

Wilhelmus Anthonius Josephus Luxemburg (Delft, 11 April 1929 – 2 October 2018)[1][2] was a Dutch American mathematician who was a professor of mathematics at the California Institute of Technology.

For the "Wilhelmus" anthem of the country called "Luxemburg", see De Wilhelmus.
WAJ Luxemburg / Late 1980's / Portrait by his son

He received his B.A. from the University of Leiden in 1950; his M.A., in 1953; his Ph.D., from the Delft Institute of Technology, in 1955. He was Assistant Professor at Caltech during 1958–60; Associate Professor, during 1960–62; Professor, during 1962–2000; Professor Emeritus, from 2000. He was the Executive Officer for Mathematics during 1970–85. In 2012 he became a fellow of the American Mathematical Society.[3] Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974.[4]

Luxemburg contributed to the development of non-standard analysis by popularizing the construction of hyperreal numbers in the 1960s. Though Edwin Hewitt had shown the construction in 1948, the formalization of non-standard analysis is generally associated with Abraham Robinson.[5]

Other notable work he did was in the theory of Riesz spaces (partially ordered vector spaces where the order structure is a lattice).[6]

Selected publications
  • 1955: Banach function spaces. Thesis, Technische Hogeschool te Delft, 1955.
  • 1969: "A general theory of monads", in Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) pp. 18–86 Holt, Rinehart and Winston
  • 1971: (with Zaanen, A. C.) Riesz Spaces. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York.
  • 1976: (with Stroyan, K. D.) Introduction to the Theory of Infinitesimals. Pure and Applied Mathematics, No. 72. Academic Press
  • 1978: (with Schep, A. R.) "A Radon-Nikodym type theorem for positive operators and a dual", Nederl. Akad. Wetensch. Indag. Math. 40, no. 3, 357–375.
  • 1979: Some Aspects of the Theory of Riesz Spaces, University of Arkansas Lecture Notes in Mathematics, 4. University of Arkansas, Fayetteville, Ark.
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References
  1. Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg
  2. American Men and Women of Science (2004), Thomson Gale
  3. List of Fellows of the American Mathematical Society, retrieved 2013-02-02.
  4. "W.A.J. Luxemburg". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 8 February 2016. Retrieved 8 February 2016.
  5. Joseph Dauben (1995) Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey, Princeton University Press
  6. Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg

See also
  • Influence of non-standard analysis
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