Answer the following question: Information: - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - Jacques Dixmier ( born 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 . He 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 . After retiring as professor emeritus from the University of Paris VI , he spent five years at the Institut des Hautes Etudes 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 Dieudonne . Dixmier was an invited speaker at the International Congress of Mathematicians in 1966 at Moscow with talk Espace dual d'une algebre , ou d'un groupe localement compact and again in 1978 at Helsinki with talk Algebres enveloppantes . - Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. - The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - 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. - In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. What entity does 'jacques dixmier' has the relation 'field of work' with?
Answer:
mathematical analysis