Leonidas (''Leon'') Alaoglu (; March 19, 1914 – August 1981) was a
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
best known for
Alaoglu's theorem on the
weak-star compactness of the closed
unit ball
Unit may refer to:
General measurement
* Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law
**International System of Units (SI), modern form of the metric system
**English units, histo ...
in the
dual of a
normed space
The Ateliers et Chantiers de France (ACF, Workshops and Shipyards of France) was a major shipyard that was established in Dunkirk, France, in 1898.
The shipyard boomed in the period before World War I (1914–18), but struggled in the inter-war p ...
, also known as the
Banach–Alaoglu theorem
In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology.
A common pro ...
.
Life and work
Alaoglu was born in
Red Deer, Alberta
Red Deer is a city in Alberta, Canada, located midway on the Calgary–Edmonton Corridor. Red Deer serves central Alberta, and its key industries include health care, retail trade, construction, oil and gas, hospitality, manufacturing and educati ...
to
Greek
Greek may refer to:
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group
*Greek language, a branch of the Indo-European language family
**Proto-Greek language, the assumed last common ancestor of all kno ...
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
The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
. 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 Bourbaki(s) may refer to :
Persons and science
* Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki
* Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in the ...
to
dual topologies.
After some years teaching at
Pennsylvania State College,
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
and
Purdue University
Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...
, in 1944 he became an
operations analyst for the
United States Air Force
The United States Air Force (USAF) is the Air force, air service branch of the United States Department of Defense. It is one of the six United States Armed Forces and one of the eight uniformed services of the United States. Tracing its ori ...
. From 1953 to 1981, he worked as a senior scientist in operations research at the
Lockheed Corporation
The Lockheed Corporation was an American aerospace manufacturer. Lockheed was founded in 1926 and merged in 1995 with Martin Marietta to form Lockheed Martin. Its founder, Allan Lockheed, had earlier founded the similarly named but otherwise-u ...
in
Burbank, California
Burbank is a city in the southeastern end of the San Fernando Valley in Los Angeles County, California, United States. Located northwest of downtown Los Angeles, Burbank had a Census-estimated population of 102,755 as of 2023. The city was ...
, where he wrote numerous research reports, some of them
classified
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Music
*Classified (rapper) (born 1977), Canadian rapper
* The Classified, a 1980s American ro ...
.
During the Lockheed years, he took an active part in
seminar
A seminar is a form of academic instruction, either at an academic institution or offered by a commercial or professional organization. It has the function of bringing together small groups for recurring meetings, focusing each time on some part ...
s and other mathematical activities at
Caltech
The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...
,
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...
and
USC USC may refer to:
Education
United States
* Universidad del Sagrado Corazón, Santurce, Puerto Rico
* University of South Carolina, Columbia, South Carolina
** University of South Carolina System, a state university system of South Carolina
* ...
. After his death in 1981,
Leonidas Alaoglu Memorial Lecture Series was established at Caltech.
[
] Speakers have included
Paul Erdős
Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...
,
Irving Kaplansky
Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St And ...
,
Paul Halmos
Paul Richard Halmos (; 3 March 1916 – 2 October 2006) was a Kingdom of Hungary, Hungarian-born United States, American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operat ...
and
Hugh Woodin.
See also
*
Axiom of Choice
In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, it is possible to construct a new set by choosing one element from e ...
– The Banach–Alaoglu theorem is not provable from
ZF without use of the Axiom of Choice.
*
Banach–Alaoglu theorem
In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the weak* topology.
A common pro ...
*
Gelfand representation
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things:
* a way of representing commutative Banach algebras as algebras of continuous functions;
* the fact that for commutative C*-al ...
*
List of functional analysis topics
This is a list of functional analysis topics.
See also: Glossary of functional analysis.
Hilbert space
Functional analysis, classic results
Operator theory
Banach space examples
*Lp space
*Hardy space
*Sobolev space
*Tsirelson space
* ...
*
Superabundant number
In mathematics, a superabundant number is a certain kind of natural number. A natural number is called ''superabundant'' precisely when, for all :
:\frac < \frac
where denotes the Tychonoff's theorem
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is tra ...
*
Weak topology
In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used for the initial topology of a ...
– 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
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also rem ...
* Alaoglu, Leonidas (Ph.D. thesis, U. of Chicago, 1938). "Weak topologies of normed linear spaces" Advisor: Lawrence Graves
*
*
*
*
*
References
*
External links
*
1914 births
1981 deaths
20th-century American mathematicians
Canadian mathematicians
Canadian emigrants to the United States
University of Chicago alumni
Topologists
Functional analysts
Number theorists
Lockheed people
People from Red Deer, Alberta
Scientists from Alberta
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