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{{for|the "Wilhelmus", anthem of the country called "Luxemburg"|De Wilhelmus}}
{{for|the "Wilhelmus", anthem of the country called "Luxemburg"|De Wilhelmus}}
[[File:WAJ Luxemburg Caltech Late 1980's.jpg|thumb|WAJ Luxemburg / Late 1980's / Portrait by his son ]]
[[File:WAJ Luxemburg Caltech Late 1980's.jpg|thumb|WAJ Luxemburg / Late 1980's / Portrait by his son ]]
'''Wilhelmus Anthonius Josephus Luxemburg''' ([[Delft]], 11 April 1929 – 2 October 2018)<ref>[http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg]</ref><ref>[[American Men and Women of Science]] (2004), Thomson Gale</ref> was a Dutch American mathematician who was a professor of [[mathematics]] at the [[California Institute of Technology]].
'''Wilhelmus Anthonius Josephus Luxemburg''' ([[Delft]], 11 April 1929 – 2 October 2018)<ref>{{Cite web |url=http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US |title=Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg |access-date=2018-10-03 |archive-date=2018-10-03 |archive-url=https://web.archive.org/web/20181003220818/http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US |url-status=dead }}</ref><ref>[[American Men and Women of Science]] (2004), Thomson Gale</ref> 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]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-02.</ref> Luxemburg became a corresponding member of the [[Royal Netherlands Academy of Arts and Sciences]] in 1974.<ref>{{cite web|author= |url=https://www.knaw.nl/en/members/correspondents/4500 |archive-url=https://web.archive.org/web/20160208210408/https://www.knaw.nl/en/members/correspondents/4500 |title=W.A.J. Luxemburg |publisher=Royal Netherlands Academy of Arts and Sciences |date= |archive-date=8 February 2016 |accessdate=8 February 2016}}</ref>
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]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-02-02.</ref> Luxemburg became a corresponding member of the [[Royal Netherlands Academy of Arts and Sciences]] in 1974.<ref>{{cite web|author= |url=https://www.knaw.nl/en/members/correspondents/4500 |archive-url=https://web.archive.org/web/20160208210408/https://www.knaw.nl/en/members/correspondents/4500 |title=W.A.J. Luxemburg |publisher=Royal Netherlands Academy of Arts and Sciences |date= |archive-date=8 February 2016 |accessdate=8 February 2016}}</ref>
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Luxemburg contributed to the development of [[non-standard analysis]] by popularizing the construction of [[hyperreal number]]s in the 1960s. Though [[Edwin Hewitt]] had shown the construction in 1948, the formalization of non-standard analysis is generally associated with [[Abraham Robinson]].<ref>[[Joseph Dauben]] (1995) ''Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey'', [[Princeton University Press]]</ref>
Luxemburg contributed to the development of [[non-standard analysis]] by popularizing the construction of [[hyperreal number]]s in the 1960s. Though [[Edwin Hewitt]] had shown the construction in 1948, the formalization of non-standard analysis is generally associated with [[Abraham Robinson]].<ref>[[Joseph Dauben]] (1995) ''Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey'', [[Princeton University Press]]</ref>


Other notable work he did was in the theory of [[Riesz space]]s ([[partially ordered set|partially ordered]] [[vector space]]s where the [[order theory|order structure]] is a [[lattice (order)|lattice]]).<ref>[http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg]</ref>
Other notable work he did was in the theory of [[Riesz space]]s ([[partially ordered set|partially ordered]] [[vector space]]s where the [[order theory|order structure]] is a [[lattice (order)|lattice]]).<ref>{{Cite web |url=http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US |title=Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg |access-date=2018-10-03 |archive-date=2018-10-03 |archive-url=https://web.archive.org/web/20181003220818/http://www.udailynews.com/news/caltech-mourns-the-passing-of-wilhelmus-a-j-luxemburg/287354/US |url-status=dead }}</ref>


==Selected publications==
==Selected publications==

Revision as of 21:48, 4 May 2023

For the "Wilhelmus", anthem of the country called "Luxemburg", see De Wilhelmus.
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". 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. ^ "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". Archived from the original on 2018-10-03. Retrieved 2018-10-03.

See also

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