Leonidas Alaoglu

Early life (1914–1938) Alaoglu was born in 1914 in Red Deer, Alberta, Canada, to Greek Canadian parents. He studied mathematics at the University of Alberta. Education and mathematical career (1938–1944) In 1938, Alaoglu received his PhD from the University of Chicago. His dissertation was on Weak topologies of normed linear spaces and establishes Alaoglu's theorem. then went on to Harvard University between 1939 and 1941 and to Purdue University between 1942 and 1944. The couple would go on to have three children, raising them in the Encino district of Los Angeles as well as in Washington, D.C. In 1953, he joined the Operations Research Division of the Lockheed Corporation as a mathematician, where he worked ever since, until he eventually died in 1981. == Research ==

Topology and analysis In 1938, Alaoglu proved in his PhD thesis that, in the dual space of a Banach space under the weak-star topology, the closed unit ball is compact. His thesis was at the University of Chicago with Lawrence M. Graves. In particular, he constructed a universal Banach space, and also described how to integrate and differentiate functions which take values in an adjoint space. The second covers the case when the group is an "ergodic group", in the sense that there is an infinite series of measures on the group that is asymptotically invariant under both left-multiplication and right-multiplication. In doing so, they made use of Albert Ingham and Guido Hoheisel's result that the density of the prime numbers is the same in intervals (q, q + cq^{\theta}) for some \theta . Geometry In 1946, Alaoglu and John H. Giese constructed uniform, isohedral polyhedra that were topologically equivalent to a torus. == See also ==