George Mackey | |
|---|---|
 | |
| Born | February 1, 1916 St. Louis, Missouri, U.S. |
| Died | March 15, 2006 (2006-03-16) (aged 90) Belmont, Massachusetts, U.S. |
| Education | Rice University (BA) Harvard University (PhD) |
| Known for | Locally convex spaces Mackey theory Quantum logic Mackey topology Mackey space Mackey–Arens theorem Mackey functor Mackey–Borel structure |
| Awards | Leroy P. Steele Prize(1975) |
| Scientific career | |
| Fields | Mathematical analysis |
| Institutions | Harvard University |
| Thesis | The Subspaces of the Conjugate of an Abstract Linear Space (1942) |
| Doctoral advisor | Marshall H. Stone |
| Doctoral students | John V. Breakwell Lawrence G. Brown Paul Chernoff Edward G. Effros Calvin C. Moore Richard Palais Caroline Series John Wermer Robert Zimmer |
| Other notable students | Andrew M. Gleason |
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions toquantum logic,representation theory, andnoncommutative geometry.
Mackey earned his B.A. atRice University in 1938 and obtained hisPh.D. atHarvard University in 1942 under the direction ofMarshall H. Stone.[1] He joined the Harvard University Mathematics Department in 1943, was appointedLandon T. Clay Professor of Mathematics and Theoretical Science in 1969 and remained there until he retired in 1985.
Earlier in his career Mackey did significant work in theduality theory oflocally convex spaces, which provided tools for subsequent work in this area, includingAlexander Grothendieck's work ontopological tensor products.
Mackey was one of the pioneer workers in the intersection ofquantum logic, the theory ofinfinite-dimensionalunitary representations ofgroups, the theory ofoperator algebras andnoncommutative geometry. A central role in Mackey's work, both in the theory of group representations and inmathematical physics, was played by the concepts ofsystem of imprimitivity andinduced representations. This idea led naturally to an analysis of the representation theory ofsemi-direct products 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 ofnilpotent Lie groups using themethod of orbits developed byAlexandre Kirillov in the 1960s. His notion of "virtual subgroup", introduced in 1966 using the language ofgroupoids, had a significant influence inergodic theory.
Another essential ingredient in Mackey's work was the assignment of aBorel structure to thedual object of alocally compact group (specifically a locally compact separable metric group)G. One of Mackey's important conjectures, which was eventually solved by work ofJames Glimm onC*-algebras, was thatG istype I (meaning that all its factor representations are of type I) if and only if the Borel structure of its dual is astandard Borel space.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularlyquantum mechanics andstatistical mechanics.
Mackey was among the first five recipients ofWilliam Lowell Putnam fellowships in 1938.[2] He received theLeroy P. Steele Prize in 1975 for his articleErgodic theory and its significance for statistical mechanics and probability theory.[3]
Mackey was an elected member of theAmerican Academy of Arts and Sciences theNational Academy of Sciences and theAmerican Philosophical Society.
Lawrence G. Brown,Paul Chernoff,Edward G. Effros,Calvin Moore,Richard Palais,Caroline Series,John Wermer andRobert Zimmer have been doctoral students of Mackey.Andrew Gleason had no PhD, but considered Mackey to be his advisor.
