Gilles I. Pisier (born 18 November 1950) is a professor of mathematics at the

Pierre and Marie Curie University 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 ...

and a distinguished professor and A.G. and M.E. Owen Chair of Mathematics at the

Texas A&M University Texas A&M University (Texas A&M, A&M, or TAMU) is a public university, public, Land-grant university, land-grant, research university in College Station, Texas. It was founded in 1876 and became the flagship institution of the Texas A&M Unive ...

. He is known for his contributions to several fields of mathematics, including

functional analysis 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 defi ...

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an ex ...

, and operator theory. He has also made fundamental contributions to the theory of C*-algebras. Gilles is the younger brother of French actress Marie-France Pisier.

Research

Pisier has obtained many fundamental results in various parts of mathematical analysis.

Geometry of Banach spaces

In the "local theory of

Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

s", Pisier and Bernard Maurey developed the theory of Rademacher type, following its use in

by J. Hoffman–Jorgensen and in the characterization of

Hilbert space In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...

s among

s by S. Kwapień. Using

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...

s, Pisier proved that super-reflexive Banach spaces can be renormed with the modulus of uniform convexity having "power type". His work (with

Per Enflo Per H. Enflo (; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved mathematical problems, problems that had been considered fundamental. Three of these problems had been open problem, ...

and

Joram Lindenstrauss Joram Lindenstrauss ( he, יורם לינדנשטראוס) (October 28, 1936 – April 29, 2012) was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics. Biogra ...

) on the "three–space problem" influenced the work on quasi–normed spaces by Nigel Kalton.

Operator theory

Pisier transformed the area of operator spaces. In the 1990s, he solved two long-standing open problems. In the theory of

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 continuou ...

s, he solved, jointly with Marius Junge, the problem of the uniqueness of C* -norms on the

tensor product In mathematics, the tensor product V \otimes W of two vector spaces and (over the same field) is a vector space to which is associated a bilinear map V\times W \to V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otime ...

of two copies of ''B(H)'', the bounded linear operators on a

''H''. He and Junge were able to produce two such tensor norms that are nonequivalent. In 1997, he constructed an operator that was polynomially bounded but not similar to a

contraction Contraction may refer to: Linguistics * Contraction (grammar), a shortened word * Poetic contraction, omission of letters for poetic reasons * Elision, omission of sounds ** Syncope (phonology), omission of sounds in a word * Synalepha, merged ...

, answering a famous question of

Paul Halmos Paul Richard Halmos ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator ...

Awards

He was an invited speaker at the 1983 ICM and a plenary speaker at the 1998 ICM. In 1997, Pisier received the

Ostrowski Prize The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Al ...

for this work. He is also a recipient of the Grands Prix de l'Académie des Sciences de Paris in 1992 and the

Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fou ...

in 1979. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meeting ...

Books

Pisier has authored several books and monographs in the fields of

, and operator theory. Among them are: * * * * * *

References

External links

* * * {{DEFAULTSORT:Pisier, Gilles 1950 births Living people 20th-century French mathematicians 21st-century French mathematicians Academic staff of the University of Paris École Polytechnique alumni Members of the French Academy of Sciences Texas A&M University faculty Fellows of the American Mathematical Society Foreign Fellows of the Indian National Science Academy