Positivity (2010) 14:567–575
W. A. J. Luxemburg: a remarkable mathematician
P. G. Dodds
Received: 19 January 2010 / Accepted: 2 August 2010
© Springer Basel AG 2010
Abstract This is an article describing some of the mathematical contributions of
W. A. J. Luxemburg.
Keywords Banach function spaces · Orlicz spaces · Positive operators ·
Mathematics Subject Classiﬁcation (2000) Primary 01A70
Positivity VI celebrates the 80th birthday of Wilhelmus Anthonius Josephus Luxem-
burg, a truly remarkable mathematician, whose work has been, and continues to be,
the source of much inspiration.
W. A. J. Luxemburg (or Wim, as he is known) was born in 1929, in the Neth-
erlands, in the city of Delft, so beautifully captured in the wonderful landscape of
Johannes Vermeer, with its images of towering spires, waterfront and the luminous
clouds sweeping across the canvas, breathing life into a vision of peace. Without doubt,
the rich cultural and artistic heritage into which Wim was born led to his lifelong pas-
sion for art; so also the rich scientiﬁc traditions that contributed to his mathematical
and scientiﬁc formation at the University of Leiden and at Delft University of Technol-
ogy (where he wrote his PhD under the guidance of A. C. Zaanen) laid the foundation
This article is an edited version of an invited talk given by the author at the conference Positivity VI in
honour of W. A. J. Luxemburg.
To Wim Luxemburg on the occasion of his 80th birthday.
P. G. Dodds (
School of Computer Science, Mathematics and Engineering,
Flinders University, GPO Box 2100, Adelaide 5001, Australia