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{{short description|Dutch American mathematician}}
{{for|the "Wilhelmus" anthem of the country called "Luxemburg"|De Wilhelmus}}
{{for|the "Wilhelmus", anthem of the country called "Luxemburg"|De Wilhelmus}}
{{Multiple issues|
[[File:WAJ Luxemburg Caltech Late 1980's.jpg|thumb|Luxemburg in the late 1980s]]
{{sources|date=December 2015}}
{{primary sources|date=December 2015}}
}}


'''Wilhelmus Anthonius Josephus Luxemburg''' (11 April 1929, in [[Delft]], [[Netherlands]] – 2018)<ref>[[American Men and Women of Science]] (2004), Thomson Gale</ref> is Professor of [[Mathematics]], Emeritus at the California Institute of Technology.
'''Wilhelmus Anthonius Josephus Luxemburg''' (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>


[[Joseph Dauben]] (1995) attributes the [[ultrapower]] construction of the [[hyperreal number]]s to Luxemburg in 1962.<ref>[[Joseph Dauben]] (1995) [[Abraham Robinson]], The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey (Princeton, N.J.: Princeton University Press, 1995).</ref> Such a construction was originally introduced by [[Edwin Hewitt]] in 1948, and popularized by Luxemburg in the 1960s.
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>{{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==
⚫
* 1955: ''Banach function spaces''. Thesis, Technische Hogeschool te Delft, 1955.
⚫
* Luxemburg, W. A. J.; [[Adriaan Cornelis Zaanen|Zaanen, A. C.]] (1971) Riesz spaces. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York.
⚫
* 1969: "A general theory of monads", in ''Applications of Model Theory to Algebra, Analysis, and Probability'' (Internat. Sympos., Pasadena, Calif., 1967) pp.&nbsp;18–86 [[Holt, Rinehart and Winston]]
⚫
* Luxemburg, Wilhelmus Anthonius Josephus (1955) Banach function spaces. Thesis, Technische Hogeschool te Delft, 1955.
⚫
* 1971: (with [[Adriaan Cornelis Zaanen|Zaanen, A. C.]]) ''Riesz Spaces''. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York.
* [[Keith Stroyan|Stroyan, K. D.]]; Luxemburg, W. A. J. (1976) Introduction to the theory of infinitesimals. Pure and Applied Mathematics, No. 72. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London.
* 1976: (with [[Keith Stroyan|Stroyan, K. D.]]) ''Introduction to the Theory of Infinitesimals''. Pure and Applied Mathematics, No. 72. [[Academic Press]]
⚫
* Luxemburg, W. A. J. (1969) A general theory of monads. 1969 Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) pp.&nbsp;18–86 Holt, Rinehart and Winston, New York.
* Luxemburg, W. A. J.; Schep, A. R. (1978) A Radon-Nikodym type theorem for positive operators and a dual. Nederl. Akad. Wetensch. Indag. Math. 40, no. 3, 357—375.
* 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.
* Luxemburg, W. A. J. (1979) Some aspects of the theory of Riesz spaces. University of Arkansas Lecture Notes in Mathematics, 4. University of Arkansas, Fayetteville, Ark.
* 1979: ''Some Aspects of the Theory of Riesz Spaces'', University of Arkansas Lecture Notes in Mathematics, 4. [[University of Arkansas]], Fayetteville, Ark.


==References==
==References==
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{{DEFAULTSORT:Luxemburg, Wilhelmus}}
{{DEFAULTSORT:Luxemburg, Wilhelmus}}
[[Category:20th-century Dutch mathematicians]]
[[Category:21st-century Dutch mathematicians]]
[[Category:American people of Dutch descent]]
[[Category:20th-century American mathematicians]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:21st-century American mathematicians]]

Latest revision as of 13:39, 21 August 2023

For the "Wilhelmus", anthem of the country called "Luxemburg", see De Wilhelmus.
Luxemburg in the late 1980s

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.

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. ^ "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.
[edit]

See also

[edit]
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