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Wilhelmus Luxemburg

Wilhelmus Anthonius Josephus Luxemburg (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.

Luxemburg in the late 1980s

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 edit

  • 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 edit

  1. ^ . Archived from the original on 2018-10-03. Retrieved 2018-10-03.
  2. ^ American Men and Women of Science (2004), Thomson Gale
  3. ^ List of Fellows of the American Mathematical Society, retrieved 2013-02-02.
  4. ^ . 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. ^ . Archived from the original on 2018-10-03. Retrieved 2018-10-03.

External links edit

See also edit

wilhelmus, luxemburg, wilhelmus, anthem, country, called, luxemburg, wilhelmus, wilhelmus, anthonius, josephus, luxemburg, april, 1929, october, 2018, dutch, american, mathematician, professor, mathematics, california, institute, technology, luxemburg, late, 1. For the Wilhelmus anthem of the country called Luxemburg see De Wilhelmus Wilhelmus Anthonius Josephus Luxemburg 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 Luxemburg in the late 1980s 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 Contents 1 Selected publications 2 References 3 External links 4 See alsoSelected publications edit1955 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 edit Caltech Mourns the Passing of Wilhelmus A J Luxemburg Archived from the original on 2018 10 03 Retrieved 2018 10 03 American Men and Women of Science 2004 Thomson Gale List of Fellows of the American Mathematical Society retrieved 2013 02 02 W A J Luxemburg Royal Netherlands Academy of Arts and Sciences Archived from the original on 8 February 2016 Retrieved 8 February 2016 Joseph Dauben 1995 Abraham Robinson The Creation of Nonstandard Analysis A Personal and Mathematical Odyssey Princeton University Press Caltech Mourns the Passing of Wilhelmus A J Luxemburg Archived from the original on 2018 10 03 Retrieved 2018 10 03 External links editWilhelmus Luxemburg at the Mathematics Genealogy ProjectSee also editInfluence of non standard analysis Retrieved from https en wikipedia org w index php title Wilhelmus Luxemburg amp oldid 1171500113, wikipedia, wiki, book, books, library,

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