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Leonidas Alaoglu (March 19, 1914 – August, 1981) was a Canadian mathematician of Greek descent, born in Red Deer, Alberta, who lived for many years in the Los Angeles area. 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 was entitled Weak topologies of normed linear spaces. His advisor was Lawrence M. Graves.

His doctoral thesis is the source of the 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. 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 and Paul Halmos.

Contents 1 How to improve your calculus textbook 2 See also 3 Publications 4 References

Saunders Mac Lane tells a story about Leon Alaoglu at Harvard, where he was teaching a beginning calculus class. Mac Lane and Alaoglu shared a low opinion of William F. Osgood's calculus book. This scene took place in the early 1940s:

"I [had] recommended the appointment of one Leonidas Alaoglu, Ph.D. Chicago, whose merits were known to me... So on one late October day Leon came to his class in Sever Hall, 'Gentlemen, we now come to Chapter IV, differentials and infinitesimals. Take pages 138 to 184 between the thumb and fingers of the right hand. Tear them from the book!' He did so."

• 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. MR0001455. 

• Alaoglu, Leonidas; and J. H. Giese (1946). "Uniform icosahedral tori". American Mathematical Monthly 53: 14-17. MR0014230. 

• Alaoglu, Leonidas; and Paul Erdős (1944). "On highly composite and similar numbers". Transactions of the American Mathematical Society 56: 448-469. MR0011087. 

• Alaoglu, Leonidas; and Paul Erdős (1944). "A conjecture in elementary number theory". Bulletin of the American Mathematical Society 50: 881-882. MR0011086. 

• Alaoglu, Leonidas; and Garrett Birkhoff (1940). "General ergodic theorems". Annals of Mathematics 41 (2): 252-267. 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.