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Leonidas Alaoglu (March 19, 1914 – August 1981) was a Canadian-American mathematician, most famous for his widely-cited result called 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 thesis, written under the direction of Lawrence M. Graves was entitled Weak topologies of normed linear spaces. His doctoral thesis is the source of 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. In his last position, from 1953 to 1981 he worked as a senior scientist in operations research at the Lockheed Corporation in Burbank, California. In this latter period 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 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.


* 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. MR0001455.
* Alaoglu, Leonidas; and J. H. Giese (1946). "Uniform isohedral tori". American Mathematical Monthly 53 (1): 14–17. doi:10.2307/2306079. MR0014230.
* Alaoglu, Leonidas; and Paul Erdős (1944). "On highly composite and similar numbers" ([dead link] – Scholar search). Transactions of the American Mathematical Society 56 (3): 448–469. doi:10.2307/1990319. MR0011087.
* Alaoglu, Leonidas; and Paul Erdős (1944). "A conjecture in elementary number theory". Bulletin of the American Mathematical Society 50: 881–882. doi:10.1090/S0002-9904-1944-08257-8. MR0011086.
* Alaoglu, Leonidas; and Garrett Birkhoff (1940). "General ergodic theorems" ([dead link] – Scholar search). Annals of Mathematics (The Annals of Mathematics, Vol. 41, No. 2) 41 (2): 252–267. doi:10.2307/1969004. MR0002026.


* American Men & Women of Science. 14th edition. New York: R.R. Bowker, 1979. There is no entry for him in the 15th or later editions.
* Apostol, Tom, emeritus professor at Caltech. Email communication that explained Alaoglu's connection to Caltech and the origins of the Leonidas Alaoglu Memorial Lecture Series.
* Mac Lane, Saunders (December 1996). "Letter to the editor". Notices of the American Mathematical Society: 1469–1471.


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