George Mackey

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George Mackey
Mackey theory
Quantum logic
Mackey topology
Mackey space
Mackey–Arens theorem
Mackey–Borel structure
AwardsLeroy P. Steele Prize (1975)
Scientific career
FieldsMathematical analysis
InstitutionsHarvard University
Thesis The Subspaces of the Conjugate of an Abstract Linear Space  (1942)
Doctoral advisorMarshall H. Stone
Doctoral studentsJohn V. Breakwell
Lawrence G. Brown
Paul Chernoff
Edward G. Effros
Calvin C. Moore
Richard Palais
Caroline Series
John Wermer
Robert Zimmer
Other notable studentsAndrew M. Gleason

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 Ph.D. at Harvard University in 1942 under the direction of Marshall H. Stone.[1] 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

locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products
.

Mackey was one of the pioneer workers in the intersection of

method of orbits developed by Alexandre Kirillov in the 1960s. His notion of "virtual subgroup", introduced in 1966 using the language of groupoids, had a significant influence in ergodic theory
.

Another essential ingredient in Mackey's work was the assignment of a Borel structure to the 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*-algebras, was that G is type I (meaning that all its factor representations are of type I) if and only if the Borel structure of its dual is a standard Borel space.

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

Honours and students

Mackey was among the first five recipients of

William Lowell Putnam fellowships in 1938.[2] He received the Leroy P. Steele Prize in 1975 for his article Ergodic theory and its significance for statistical mechanics and probability theory.[3]

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

Andrew Gleason
had no PhD, but considered Mackey to be his advisor.

Books

See also

References

  1. ^ "George Mackey - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved 2024-01-09.
  2. ^ "Putnam Competition Individual and Team Winners". Mathematical Association of America. Retrieved December 9, 2021.
  3. doi:10.1016/S0001-8708(74)80003-4
    .
  4. doi:10.1090/s0002-9904-1967-11717-8
    .
  5. ^ Berg, Michael (November 19, 2004). "Joint review of Mathematical Foundations of Quantum Mechanics by George W. Mackey; A Taste of Jordan Algebras by Kevin McCrimmon". MAA Review, Mathematical Association of America.
  6. doi:10.1090/s0273-0979-1980-14731-x
    .
  7. doi:10.1090/s0002-9904-1978-14410-3
    .

External links
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