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 o ...
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 contin ...
s, and wrote several of the standard reference books on them, and introduced the
Dixmier trace and the
Dixmier mapping.
Biography
Dixmier received his
Ph.D. in 1949 from the
University of Paris
The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
, and his students include
Alain Connes
Alain Connes (; born 1 April 1947) is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He was a professor at the , , Ohio State University and Vanderbilt University. He was awar ...
.
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 inau ...
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 Bourbaki(s) may refer to :
Persons and science
* Charles-Denis Bourbaki (1816–1897), French general, son of Constantin Denis Bourbaki
* Colonel Constantin Denis Bourbaki (1787–1827), officer in the Greek War of Independence and serving in the ...
, 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 operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...
s.
After retiring as professor emeritus from the
University of Paris VI
Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, ...
, 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 (also with a small theoretical biology g ...
.
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 al ...
'' for the operator algebras introduced by
John von Neumann
John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
, 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 pseudonymous ...
.
Dixmier was an
invited speaker at the International Congress of Mathematicians
An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...
in 1966 in
Moscow
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...
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.
:: 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
*
See also
*
Dixmier–Ng theorem
Notes
1924 births
Living people
École Normale Supérieure alumni
20th-century French mathematicians
21st-century French mathematicians
French mathematical analysts
University of Paris alumni
Nicolas Bourbaki
Scientists from Saint-Étienne
Academic staff of the University of Paris
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