Wilhelmus A. J. Luxemburg
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Wilhelmus A. J. Luxemburg
WAJ Luxemburg / Late 1980's / Portrait by his son

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.

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.

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 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

External links

See also


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