Jacques Dixmier

{{Infobox scientist

| name = Jacques Dixmier

| image =

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| caption =

| birth_date = {{b-da|24 May 1924}}

| birth_place = Saint-Étienne, France

| death_date =

| death_place =

| fields = Mathematics

| workplaces = University of Paris

| alma_mater = University of Paris

| doctoral_advisor = Gaston Julia

| doctoral_students = Alain Connes
Michel Duflo
Michèle Vergne
Nicole Berline

| thesis_title = Étude sur les variétés et les opérateurs de Julia avec quelques applications{{MathGenealogy|id=34272}}

| known_for = Dixmier condition
Dixmier conjecture
Dixmier mapping
Dixmier problem
Dixmier trace

| awards = Prix de l'État (1962)
Prix Ampère (1976)
Leroy P. Steele Prize (1992)
Émile-Picard-Medaille (2001)

}}

Jacques Dixmier (born 24 May 1924) is a French mathematician. He worked on operator algebras, especially C*-algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace and the Dixmier mapping.{{cite book |editor1-last=Turkevich |editor1-first=Ludmilla Buketoff |editor2-last=Turkevich |editor2-first=John |title=Prominent Scientists of Continental Europe |date=1968 |publisher=American Elsevier Publishing Company |isbn=9780444000460 |page=43 |url=https://books.google.com/books?id=BEO7qf4NbooC&q=Jacques+Dixmier++1924 |access-date=9 March 2021}}

Biography

Dixmier received his Ph.D. in 1949 from the University of Paris, and his students include Alain Connes.

In 1949 upon the initiative of Jean-Pierre Serre and Pierre Samuel, Dixmier became a member of Bourbaki, in which he made essential contributions to the Bourbaki volume on Lie algebras.{{cite news|newspaper=Newsletter of the EMS|date=June 2009|title=Interview with Jacques Dixmier|page=38}} After retiring as professor emeritus from the University of Paris VI, he spent five years at the Institut des Hautes Études Scientifiques.

Often, there is made the erroneous claim that Dixmier originated the name von Neumann algebra for the operator algebras introduced by John von Neumann, but Dixmier said in an interview that the name originated from a proposal by Jean Dieudonné.

Dixmier was an invited speaker at the International Congress of Mathematicians in 1966 in Moscow with the talk Espace dual d'une algèbre, ou d'un groupe localement compact and again in 1978 in Helsinki with the talk Algèbres enveloppantes.

Publications

J. Dixmier, C*-algebras. Translated from the French by Francis Jellett. North-Holland Mathematical Library, Vol. 15. North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. xiii+492 pp. {{ISBN|0-7204-0762-1}}

:: A translation of Les C*-algèbres et leurs représentations, Gauthier-Villars, 1969.

{{Citation | last1=Dixmier | first1=Jacques | title=Enveloping algebras | orig-year=1974 | url=https://books.google.com/books?isbn=0821805606 | publisher=American Mathematical Society | location=Providence, R.I. | series=Graduate Studies in Mathematics | isbn=978-0-8218-0560-2 | mr=0498740 | year=1996 | volume=11}}

:: A translation of Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII. Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974. ii+349 pp.

J. Dixmier, von Neumann algebras, Translated from the second French edition by F. Jellett. North-Holland Mathematical Library, 27. North-Holland Publishing Co., Amsterdam-New York, 1981. xxxviii+437 pp. {{ISBN|0-444-86308-7}}

::A translation of Les algèbres d'opérateurs dans l'espace hilbertien: algèbres de von Neumann, Gauthier-Villars (1957), the first book about von Neumann algebras.