Mischa Cotlar

Encounters with Mischa Cotlar John Horváth Before I begin my tale, I want to call the reader’s attention to the volumeAnalysis and Partial Dif- ferential Equations[20], edited by Cora Sadosky in honor of the seventieth birthday of Mischa Cotlar. There can be found the biography of Mischa, three essays about his personality, an analysis of his mathematical works, and the list of his publications until 1989. The First Encounter From 1948 to 1951 I lived in theColegio de España at the University City in Paris. Since the Spanish civil war the college was under the administration of the French government and housed several refugees from Spain. Among them there were some mathematicians who had settled in Argentina, for instance Manuel Balanzat, professor at the University of Cuyo in San Luis and a disciple of Luis A. Santaló. I must add that I had already heard about Santaló in Budapest in 1946 when László Fejes-Tóth presented Santaló’s proof of the isoperimetric inequality in his course on geometry. There were also some Portuguese mathemati- cians, opposed to the Salazar regime and estab- lished in Brazil. It is from all these that I first heard the names of Antonio Monteiro, Leopoldo Nachbin, and Mischa Cotlar. In May 1951, on my way from Paris to Bogotá, I visited the United States for a few weeks. With my fellow student Steve Gaal we traveled to New Haven to see Shizuo Kakutani at Yale University. John Horváth is professor emeritus of mathematics at the University of Maryland, College Park. His email address is [email protected]. Translation from the Spanish of the article that will ap- pear in theBulletin of the Mexican Mathematical Society, Volume 15, No. 1, 2009. Used with permission of the Mexican Mathematical Society. Mischa Cotlar in Chicago, 1952. Kakutani told us that Cotlar was in New Haven, supported by a Guggenheim fel- lowship and with the intention of ob- taining a Ph.D. in mathematics from Yale. Kakutani gave us some information about Mischa’s life: That he had arrived in Uruguay from Russia as a child, that later on he had earned a living playing the pi- ano in the dives of the port of Montevideo, that he never went to school. Kakutani added that Mischa was a self-taught mathematician who had been publishing articles since 1936, when he was twenty-three years old. Cotlar’s interest in ergodic theory had brought him to New Haven, to study with Kakutani. Indeed, Kakutani was considered at that time the foremost expert in the subject, so much so that he undertook to give a panoramic lecture on it at the Internation- al Congress of Mathematicians held in 1950 in Cambridge, Massachusetts [17]. I recall an amusing detail from those times before Xerox machines, before computers, and before email: Kakutani had a single copy of the text of his lecture, which had not yet been published. I asked him to lend it to me, which he did after I swore to return it. Going back to May 1951, Cotlar came to dinner with us and afterwards, I witnessed the first exam- ple of his unbelievable humility. I had to return to New York, and the colleagues accompanied me to the railroad station. Cotlar, who was eleven years older than I, insisted on carrying my suitcase! After 616Notices of the AMSVolume56, Number5 additive monotone functions on partially ordered semi-groups, can be generalized without essential change of the method of proof and so obtain a notable round out form.” In my lecture I mentioned this reference to the work of Cotlar, and after the class Carlos Berenstein, who had just received his Ph.D. with Leon Ehrenpreis, came to talk with me. He told me that he was Argentinean and that there were other Argentineans in the audience who all were happy to hear Cotlar’s name quoted. I must add that after this summer school, Benno Fuchssteiner furthered the theory of operators on ordered semi-groups. His results can be found in [16], as well as in the Lecture Notes ([24], pp. 45–46) and in the updated edition of the book on topological v