Leonidas Alaoglu

Leonidas Alaoglu
Born	(1914-03-19)March 19, 1914 Red Deer, Alberta
Died	August 1981 (1981-09) (aged 67)
Citizenship	Canadian-American
Education	University of Chicago
Known for	Alaoglu's theorem
Scientific career
Fields	Mathematics (Topology)
Institutions	Pennsylvania State College Harvard University Purdue University United States Air Force Lockheed Martin
Thesis	Weak topologies of Normed linear spaces  (1938)
Doctoral advisor	Lawrence M. Graves

Leonidas (Leon) Alaoglu (Greek: Λεωνίδας Αλάογλου; March 19, 1914 – August 1981) was a mathematician best known for Alaoglu's theorem on the weak-star compactness of the closed unit ball in the dual of a normed space, also known as the Banach–Alaoglu theorem.

Life and work

Alaoglu was born in Red Deer, Alberta to Greek parents. He received his BS in 1936, Master's in 1937, and PhD in 1938 (at the age of 24), all from the University of Chicago. His dissertation, written under the direction of Lawrence M. Graves, was on Weak topologies of normed linear spaces and establishes Alaoglu's theorem. The Bourbaki–Alaoglu theorem is a generalization of this result by Bourbaki to dual topologies.

After some years teaching at Pennsylvania State College, Harvard University and Purdue University, in 1944 he became an operations analyst for the United States Air Force. From 1953 to 1981, he worked as a senior scientist in operations research at the Lockheed Corporation in Burbank, California, where he wrote numerous research reports, some of them classified.

During the Lockheed years, he took an active part in seminars and other mathematical activities at Caltech, UCLA and USC. After his death in 1981, a Leonidas Alaoglu Memorial Lecture Series Archived 2020-08-06 at the Wayback Machine was established at Caltech. Speakers have included Paul Erdős, Irving Kaplansky, Paul Halmos and Hugh Woodin.

See also

• Axiom of Choice – The Banach–Alaoglu theorem is not provable from ZF without use of the Axiom of Choice.
• Banach–Alaoglu theorem
• Gelfand representation
• List of functional analysis topics
• Superabundant number – Article explains the 1944 results of Alaoglu and Erdős on this topic
• Tychonoff's theorem
• Weak topology – Leads to the weak-star topology to which the Banach–Alaoglu theorem applies.

Publications

• Alaoglu, Leonidas (M.S. thesis, U. of Chicago, 1937). "The asymptotic Waring problem for fifth and sixth powers" (24 pages). Advisor: Leonard Eugene Dickson
• Alaoglu, Leonidas (Ph.D. thesis, U. of Chicago, 1938). "Weak topologies of normed linear spaces" Advisor: Lawrence Graves
• Alaoglu, Leonidas (1940). "Weak topologies of normed linear spaces". Annals of Mathematics. 41 (2): 252–267. doi:10.2307/1968829. JSTOR 1968829. MR 0001455.
• Alaoglu, Leonidas; J. H. Giese (1946). "Uniform isohedral tori". American Mathematical Monthly. 53 (1): 14–17. doi:10.2307/2306079. JSTOR 2306079. MR 0014230.
• Alaoglu, Leonidas; Paul Erdős (1944). "On highly composite and similar numbers" (PDF). Transactions of the American Mathematical Society. 56 (3): 448–469. doi:10.2307/1990319. JSTOR 1990319. MR 0011087.
• Alaoglu, Leonidas; Paul Erdős (1944). "A conjecture in elementary number theory". Bulletin of the American Mathematical Society. 50 (12): 881–882. doi:10.1090/S0002-9904-1944-08257-8. MR 0011086.
• Alaoglu, Leonidas; Garrett Birkhoff (1940). "General ergodic theorems". Annals of Mathematics. 41 (2): 252–267. doi:10.2307/1969004. JSTOR 1969004. MR 0002026. PMC 1077986. PMID 16588311.

References

• Mac Lane, Saunders (December 1996). "Letter to the editor" (PDF). Notices of the American Mathematical Society: 1469–1471.

External links

• Leonidas Alaoglu at the Mathematics Genealogy Project