Editing George Mackey

{{Short description|American mathematician}}
{{Infobox scientist
| name              = George Mackey
| image             = GWMackey c1980s.jpg
| birth_date        = February 1, 1916  <!-- {{birth date and age|YYYY|MM|DD}}  -->
| birth_place       = [[St. Louis, Missouri|St. Louis]], [[Missouri]], U.S.
| death_date        = {{d-da|March 15, 2006|February 1, 1916}}
| death_place       = [[Belmont, Massachusetts|Belmont]], [[Massachusetts]], U.S.
| fields            = [[Mathematical analysis]]
| workplaces        = [[Harvard University]]
| education        = [[Rice University]] ([[B. A.|BA]])<br> [[Harvard University]] ([[PhD]])<!-- will often consist of the linked name of the last-attended higher education institution. -->
| thesis_title      = The Subspaces of the Conjugate of an Abstract Linear Space
| thesis_year       = 1942
| doctoral_advisor  = [[Marshall H. Stone]]
| doctoral_students = [[John V. Breakwell]]<br>[[Lawrence G. Brown]]<br>[[Paul Chernoff]]<br>[[Edward George Effros|Edward G. Effros]]<br>[[Calvin C. Moore]]<br>[[Richard Palais]]<br>[[Caroline Series]]<br>[[John Wermer]]<br>[[Robert Zimmer]]
| notable_students  = [[Andrew M. Gleason]]<!--Only those with WP articles-->
| known_for         = [[Locally convex space]]s<br>[[Mackey theory]]<br />[[Quantum logic]]<br />[[Mackey topology]]<br />[[Mackey space]]<br />[[Mackey–Arens theorem]]<br/>[[Mackey functor]]<br />[[Spectrum_of_a_C*-algebra#Mackey–Borel_structure|Mackey–Borel structure]]
| awards            = [[Leroy P. Steele Prize]] {{small|(1975)}}
}}

'''George Whitelaw Mackey''' (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to [[quantum logic]], [[representation theory]], and [[noncommutative geometry]].

==Career==
Mackey earned his B.A. at [[Rice University]] in 1938 and obtained his [[Doctor of Philosophy|Ph.D.]] at [[Harvard University]] in 1942 under the direction of [[Marshall H. Stone]].<ref>{{Cite web |title=George Mackey - The Mathematics Genealogy Project |url=https://www.mathgenealogy.org/id.php?id=22868 |access-date=2024-01-09 |website=www.mathgenealogy.org}}</ref> He joined the Harvard University Mathematics Department in 1943, was appointed [[Landon T. Clay]] Professor of Mathematics and Theoretical Science in 1969 and remained there until he retired in 1985.

==Work==
Earlier in his career Mackey did significant work in the [[duality theory]] of [[locally convex space]]s, which provided tools for subsequent work in this area, including [[Alexander Grothendieck]]'s work on [[topological tensor product]]s.

Mackey was one of the pioneer workers in the intersection of [[quantum logic]], the theory of [[dimension (vector space)|infinite-dimensional]] [[unitary representation]]s of [[group (mathematics)|group]]s, the theory of [[operator algebra]]s and [[noncommutative geometry]]. A central role in Mackey's work, both in the theory of group representations and in [[mathematical physics]], was played by the concepts of [[system of imprimitivity]] and [[induced representation]]s. This idea led naturally to an analysis of the representation theory of [[semi-direct product]]s in terms of ergodic actions of groups and in some cases a complete classification of such representations. Mackey's results were essential tools in the study of the representation theory of [[nilpotent group|nilpotent Lie group]]s using the [[kirillov orbit theory|method of orbits]] developed by [[Alexandre Kirillov]] in the 1960s. His notion of "virtual subgroup", introduced in 1966 using the language of [[groupoid]]s, had a significant influence in [[ergodic theory]].

Another essential ingredient in Mackey's work was the assignment of a [[Borel set|Borel structure]] to the [[Spectrum of a C*-algebra|dual object]] of a [[locally compact group]] (specifically a locally compact separable metric group) ''G''. One of Mackey's important conjectures, which was eventually solved by work of [[James Glimm]] on [[C*-algebra]]s, was that ''G'' is [[von Neumann algebra#Type I factors|type I]] (meaning that all its factor representations are of type I) if and only if the Borel structure of its dual is a [[Borel set#Standard Borel spaces and Kuratowski theorems|standard Borel space]].

He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly [[mathematical formulation of quantum mechanics|quantum mechanics]] and [[statistical mechanics]].

==Honours and students==
Mackey was among the first five recipients of [[Putnam exam|William Lowell Putnam]] fellowships in 1938.<ref name="MMA">{{cite web|title=Putnam Competition Individual and Team Winners |url=http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |publisher=[[Mathematical Association of America]]|access-date=December 9, 2021}}</ref> He received the [[Leroy P. Steele Prize]] in 1975 for his article ''Ergodic theory and its significance for statistical mechanics and probability theory''.<ref>{{cite journal
| first1=George W. | last1=Mackey
| title=Ergodic theory and its significance for statistical mechanics and probability theory
| journal=[[Advances in Mathematics]]
| volume=12
| issue=2
| year=1974
| pages=178–268
| doi=10.1016/S0001-8708(74)80003-4 | doi-access=free}}</ref>

Mackey was an elected member of the [[American Academy of Arts and Sciences]] the [[National Academy of Sciences]] and the [[American Philosophical Society]].

[[Lawrence G. Brown]], [[Paul Chernoff]], [[Edward George Effros|Edward G. Effros]], [[Calvin C. Moore|Calvin Moore]], [[Richard Palais]], [[Caroline Series]], [[John Wermer]] and [[Robert Zimmer]] have been doctoral students of Mackey. [[Andrew Gleason]] had no PhD, but considered Mackey to be his advisor.

==Books==
*''Mathematical Foundations of Quantum Mechanics''<ref>{{cite journal|author=Feldman, Jacob|title=Review: ''Foundations of quantum mechanics'', by G. Mackey|journal=[[Bulletin of the American Mathematical Society]]|year=1967|volume=73|issue=4|pages=499–500|url=https://www.ams.org/journals/bull/1967-73-04/S0002-9904-1967-11717-8/|doi=10.1090/s0002-9904-1967-11717-8|doi-access=free}}</ref> (Dover Books on Mathematics, 2004 {{ISBN|0-486-43517-2}} {{ISBN|978-0-486-43517-6}})<ref>{{cite web|author=Berg, Michael|date=November 19, 2004|title=Joint review of ''Mathematical Foundations of Quantum Mechanics'' by George W. Mackey; ''A Taste of Jordan Algebras'' by Kevin McCrimmon|website=MAA Review, Mathematical Association of America|url=https://www.maa.org/press/maa-reviews/mathematical-foundations-of-quantum-mechanics}}</ref>
*''Unitary Group Representations in Physics, Probability, and Number Theory'', 402 pages, Benjamin–Cummings Publishing Company (1978), {{ISBN|0-8053-6703-9}}<ref>{{cite journal|author=Gustafson, Karl|author-link=Karl Edwin Gustafson|title=Review: ''Unitary group representations in physics, probability, and number theory'', by G. Mackey|journal=Bulletin of the American Mathematical Society | series=New Series|year=1980|volume=2|issue=1|pages=225–229|url=https://www.ams.org/journals/bull/1980-02-01/S0273-0979-1980-14731-X|doi=10.1090/s0273-0979-1980-14731-x|doi-access=free}}</ref>
*''The Theory of Unitary Group Representations'' (Chicago Lectures in Mathematics) University Of Chicago Press (August 1, 1976) {{ISBN|0-226-50051-9}}<ref>{{cite journal|last=Kunze|first=Ray A.|authorlink=Ray Kunze|title=Review: ''The theory of unitary group representations'', by G. Mackey|journal=Bulletin of the American Mathematical Society|year=1978|volume=84|issue=1|pages=73–75|url=https://www.ams.org/journals/bull/1978-84-01/S0002-9904-1978-14410-3/|doi=10.1090/s0002-9904-1978-14410-3|doi-access=free}}</ref>
*''Induced representations of groups and quantum mechanics'', Publisher: W. A. Benjamin (1968)
*''Mathematical Problems of Relativistic Physics'' (Lectures in Applied Mathematics Series, Vol 2) by [[Irving Segal|I. E. Segal]], George Whitelaw Mackey, Publisher: Amer Mathematical Society (June 1967) {{ISBN|0-8218-1102-9}}
*''Lectures on the theory of functions of a [[complex variable]]'' Publisher: R. E. Krieger Pub. Co (1977) {{ISBN|0-88275-531-5}}

== See also ==
*[[Bornological space]]

==References==
{{reflist}}

==External links==
*{{MacTutor Biography|id=Mackey}}
*{{MathGenealogy |id=22868}}
*[https://www.ams.org/notices/200707/tx070700824p.pdf George Mackey (1916–2006)], ''[[Notices of the American Mathematical Society]]''; vol. 54, no. 7 (August 2007).
*[https://web.archive.org/web/20230723072836/http://www.aps-pub.com/proceedings/1524/1520411.pdf George Mackey (1 February 1916–15 March 2006)], ''Proceedings of the American Philosophical Society''; vol. 152, no. 4 (December 2008).
*[http://www.math.harvard.edu/history/mackey/index.html Commemorative website at Harvard Math Department]
*[https://web.archive.org/web/20060513054920/http://www.news.harvard.edu/gazette/2006/04.06/20-mackeyobit.html Obituary from Harvard Gazette]
*http://archive.boston.com/news/globe/obituaries/articles/2006/04/28/george_mackey_professor_devoted_to_truth_theorems/?page=1 Obituary from Boston Globe]
*[http://www.math.columbia.edu/~woit/wordpress/?p=362 Peter Woit's blog entry on Mackey]
*Two letters from George Mackey and the text of his speech "What do Mathematicians Do?, collected by Stephanie Singer
**[https://web.archive.org/web/20110716174438/http://www.symmetrysinger.com/Mackey/letter1.pdf First letter]
**[https://web.archive.org/web/20110720031652/http://www.symmetrysinger.com/Mackey/letter2.pdf Second letter]
**[https://web.archive.org/web/20110720031727/http://www.symmetrysinger.com/Mackey/speech.pdf Speech]

{{Authority control}}

{{DEFAULTSORT:Mackey, George Whitelaw}}
[[Category:1916 births]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:2006 deaths]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:American mathematical analysts]]
[[Category:American topologists]]
[[Category:Putnam Fellows]]
[[Category:Rice University alumni]]
[[Category:Harvard University alumni]]
[[Category:Harvard University Department of Mathematics faculty]]
[[Category:People from St. Louis]]
[[Category:Mathematicians from Missouri]]
[[Category:Functional analysts]]