Wilhelmus Anthonius Josephus Luxemburg (11 April 1929 – 2 October 2018) 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 an assistant professor at Caltech from 1958-60; an associate professor from 1960–62; a professor from 1962–2000; and a 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. Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974. 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. Other notable work he did was in the theory of Riesz spaces (partially ordered vector spaces where the order structure is a lattice).
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
External links Wilhelmus Luxemburg at the Mathematics Genealogy Project
See also Influence of non-standard analysis