Jacques Dixmier (born 24 May 1924) is a French mathematician. He worked on

operator algebra In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of ...

s, especially

C*-algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous ...

s, and wrote several of the standard reference books on them, and introduced the

Dixmier trace In mathematics, the Dixmier trace, introduced by , is a non-normal trace on a space of linear operators on a Hilbert space larger than the space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmie ...

and the

Dixmier mapping In mathematics, the Dixmier mapping describes the space Prim(''U''(''g'')) of primitive ideals of the universal enveloping algebra ''U''(''g'') of a finite-dimensional solvable Lie algebra ''g'' over an algebraically closed field of characteristic ...

Biography

Dixmier received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

in 1949 from the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

, and his students include

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vande ...

. In 1949 upon the initiative of

Jean-Pierre Serre Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...

and

Pierre Samuel Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work ''Commutative Algebra'' that he wrote with Oscar Zariski ...

, Dixmier became a member of Bourbaki, in which he made essential contributions to the Bourbaki volume on

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

s. After retiring as professor emeritus from the

University of Paris VI Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the L ...

, he spent five years at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, just ...

. Often, there is made the erroneous claim that Dixmier originated the name ''

von Neumann algebra In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann algeb ...

'' for the operator algebras introduced by

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

, but Dixmier said in an interview that the name originated from a proposal by

Jean Dieudonné Jean Alexandre Eugène Dieudonné (; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymo ...

. Dixmier was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in 1966 at

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

with talk ''Espace dual d'une algèbre, ou d'un groupe localement compact'' and again in 1978 at Helsinki with 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. :: A translation of ''Les C*-algèbres et leurs représentations'', Gauthier-Villars, 1969. * :: 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. ::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.

Books

Notes

1924 births Living people École Normale Supérieure alumni 20th-century French mathematicians 21st-century French mathematicians Mathematical analysts University of Paris alumni Nicolas Bourbaki Scientists from Saint-Étienne University of Paris faculty {{France-mathematician-stub