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George Mackey 1916–2006 Robert S George Mackey 1916–2006 Robert S. Doran and Arlan Ramsay Robert S. Doran the time, were themselves fairly young Chicago Ph.D.’s. I purchased a copy of Mackey’s notes through the University of Chicago mathematics Introduction department and had them carefully bound in hard George Whitelaw Mackey died of complications cover. They became my constant companion as from pneumonia on March 15, 2006, in Belmont, I endeavored to understand this beautiful and Massachusetts, at the age of ninety. He was a re- difficult subject. In this regard it is certainly not markable individual and mathematician who made an exaggeration to say that Mackey’s notes were a lasting impact not only on the theory of infinite often the catalyst that led many mathematicians dimensional group representations, ergodic theo- to study representation theory. As one important ry, and mathematical physics but also on those example I mention J. M. G. (Michael) Fell, who, with individuals with whom he personally came into the late D. B. Lowdenslager, wrote up the original contact. The purpose of this article is to celebrate 1955 Chicago lecture notes. Fell makes it clear in and reflect on George’s life by providing a glimpse the preface of our 1988 two-volume work [1, 2] into his mathematics and his personality through on representations of locally compact groups and the eyes of several colleagues, former students, Banach *-algebraic bundles that the basic direc- family, and close friends. Each of the contributors tion of his own research was permanently altered to the article has his or her own story to tell by his experience with Mackey’s Chicago lectures. regarding how he influenced their lives and their The final chapter of the second volume treats mathematics. generalized versions of Mackey’s beautiful normal I first became aware of George Mackey forty-five subgroup analysis and is, in many respects, the years ago through his now famous 1955 Chicago apex of the entire work. It is perhaps safe to say lecture notes on group representations and also that these volumes stand largely as a tribute to through his early fundamental work on the du- George Mackey’s remarkable pioneering work on ality theory of locally convex topological vector induced representations, the imprimitivity theo- spaces. I had taken a substantial course in func- rem, and what is known today as the “Mackey tional analysis, and Mackey’s Chicago notes were Machine”. a rather natural next step resulting from my inter- In 1970 I contacted George to see if he would est in C*-algebras and von Neumann algebras—an be interested in coming to TCU (Texas Christian interest instilled in me by Henry Dye and Ster- University) to present a series of lectures on a ling Berberian, both inspiring teachers who, at topic in which he was currently interested. In spite of being very busy (at the time, as I recall, he was Robert S. Doran is Potter Professor of Mathematics at in Montecatini, Italy, giving lectures) he graciously Texas Christian University. His email address is [email protected]. accepted my invitation, and I enthusiastically sub- Arlan Ramsay is emeritus professor of mathematics at mitted a grant to the NSF for a CBMS (Conference the University of Colorado at Boulder. His email address Board of the Mathematical Sciences) conference is [email protected]. to be held at TCU with George as the principal 824 Notices of the AMS Volume 54, Number 7 lecturer. Although the grant was carefully pre- kind of mathematical argument. Perhaps this, at pared, including a detailed description provided least in part, is why he had a particularly strong by George of his ten lectures titled “Ergodic the- affinity for mathematics, a discipline where proof, ory and its significance in statistical mechanics not faith, is the order of the day. and probability theory”, the grant was not fund- Following the biography below, Calvin Moore ed. Given George’s high mathematical standing provides an overview of George’s main mathemat- and reputation, I was of course surprised when we ical contributions together with some personal were turned down. Fortunately, I was able to secure recollections. Then each of the remaining writ- funding for the conference from another source, ers shares personal and mathematical insights and in 1972 George came to TCU to take part as resulting from his or her (often close) association originally planned. True to form he showed up in with George. Arlan Ramsay and I, as organizers, Fort Worth with sport coat and tie (even though are deeply grateful to all of the writers for their it was quite hot) and with his signature clipboard contributions, and we sincerely thank them for in hand. Many of the leading mathematicians and honoring an esteemed colleague, mentor, family mathematical physicists of the day, both young member, and friend who will be greatly missed. and old, attended, and the result was a tremen- dously exciting and meaningful conference. To Biography of George W. Mackey put the cherry on top, Mackey’s ten conference George Whitelaw Mackey was born February 1, lectures were published in [3], and he received a 1916, in St. Louis, Missouri, and died on March 15, coveted AMS Steele Prize in 1975 for them. 2006, in Belmont, Massachusetts. He received a From these ear- bachelor’s degree from the Rice Institute (now Rice ly days in the University) in 1938. As an undergraduate he had 1970s George and interests in chemistry, I became good physics, and mathemat- friends, and we ics. These interests were would meet for developed during his ear- lunch on those ly high school years. occasions that we After briefly considering could get togeth- chemical engineering as a er at meetings major his freshman year and conferences (lunches are a pat- in college, he decided tern with George, instead that he wanted as you will note to be a mathematical from other writ- physicist, so he ended ers). It seemed up majoring in physics. that we agreed However, he was in- creasingly drawn to pure Photo courtesy of Ann Mackey. on most things mathematics because of George Mackey, on mathematical—he what he perceived as vacation in 1981. of course was the master, I was the a lack of mathematical student. On the other hand, he particularly liked rigor in his physics class- Photo courtesy of Ann Mackey. to debate philosophical and spiritual matters, and es. His extraordinary gift A young George Mackey. we held rather different points of view on some in mathematics became things. These differences in no way affected our particularly clear when he was recognized nation- relationship. If anything, they enhanced it. Indeed, ally as one of the top five William Lowell Putnam George honestly enjoyed pursuing ideas to the winners during his senior year at Rice. His reward very end, and he doggedly, but gently, pushed for this accomplishment was an offer of a full hard to see if one could defend a particular point scholarship to Harvard for graduate work, an offer of view. I enjoyed this too, so it usually became a that he accepted. kind of sparring match with no real winner. The He earned a master’s degree in mathematics in next time we would meet (or talk on the phone) 1939 and a Ph.D. in 1942 under the direction of it would start all over again. Although at times famed mathematician Marshall H. Stone, whose he could be somewhat brusque, he was always 1932 book Linear Transformations in Hilbert kind, compassionate, and highly respectful, and, Space had a substantial influence on his mathe- I believe, he genuinely wanted to understand the matical point of view. Through Stone’s influence, other person’s viewpoint. It seemed to me that Mackey was able to obtain a Sheldon Traveling he simply had a great deal of difficulty accepting Fellowship allowing him to split the year in 1941 statements that he personally could not establish between Cal Tech and the Institute for Advanced through careful logical reasoning or through some Study before completing his doctorate. While August 2007 Notices of the AMS 825 at the Institute he met many legendary figures, Ph.D. Students of George Mackey, among them Albert Einstein, Oswald Veblen, and Harvard University John von Neumann, as well as a host of young Ph.D.’s such as Paul Halmos, Warren Ambrose, Lawrence Brown, 1968 Valentine Bargmann, Paul Erdos,˝ and Shizuo Paul Chernoff, 1968 Kakutani. Lawrence Corwin, 1968 After receiving his Ph.D. he spent a year on the Edward Effros, 1962 faculty at the Illinois Institute of Technology and Peter Forrest, 1972 then returned to Harvard in 1943 as an instruc- Andrew Gleason, 1950 tor in the mathematics department and remained Robert Graves, 1952 there until he retired in 1985. He became a full Peter Hahn, 1975 professor in 1956 and was appointed Landon T. Christopher Henrich, 1968 Clay Professor of Mathematics and Theoretical John Kalman, 1955 Science in 1969, a position he retained until he Adam Kleppner, 1960 retired. M. Donald MacLaren, 1962 His main areas of research were in repre- Calvin Moore, 1960 sentation theory, group actions, ergodic theory, Judith Packer, 1982 functional analysis, and mathematical physics. Richard Palais, 1956 Much of his work involved the interaction be- Arlan Ramsay, 1962 tween infinite-dimensional group representations, Caroline Series, 1976 the theory of operator algebras, and the use of Francisco Thayer, 1972 quantum logic in the mathematical foundations Seth Warner, 1955 of quantum mechanics. His notion of a system of John Wermer, 1951 imprimitivity led naturally to an analysis of the Thomas Wieting, 1973 representation theory of semidirect products in Neal Zierler, 1959 terms of ergodic actions of groups.
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