Gilles Pisier
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Gilles I. Pisier (born 18 November 1950) is a professor of mathematics at the
Pierre and Marie Curie University 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, ...
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, TA&M, or TAMU) is a public university, public, Land-grant university, land-grant, research university in College Station, Texas, United States. It was founded in 1876 and became the flagship institution of ...
. 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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...
,
probability theory Probability theory or probability calculus 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 expre ...
,
harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
, and
operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operato ...
. He has also made fundamental contributions to the theory of C*-algebras. Gilles is the younger brother of French actress
Marie-France Pisier Marie-France Pisier (10 May 194424 April 2011) was a French actress, screenwriter, and director. She appeared in numerous films of the French New Wave, and twice earned the national César Award for César Award for Best Supporting Actress, Best ...
.


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 (, ) 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 vectors and ...
s", Pisier and Bernard Maurey developed the theory of Rademacher type, following its use in
probability theory Probability theory or probability calculus 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 expre ...
by J. Hoffman–Jorgensen and in the characterization of
Hilbert space In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
s among
Banach space In mathematics, more specifically in functional analysis, a Banach space (, ) 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 vectors and ...
s by S. Kwapień. Using
probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
in
vector space In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called sc ...
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 and Joram Lindenstrauss) 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 contin ...
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 V and W (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of ...
of two copies of ''B(H)'', the bounded linear operators on a
Hilbert space In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
 ''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, answering a famous question of
Paul Halmos Paul Richard Halmos (; 3 March 1916 – 2 October 2006) was a Kingdom of Hungary, Hungarian-born United States, American mathematician and probabilist who made fundamental advances in the areas of mathematical logic, probability theory, operat ...
.


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 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 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, meetings, ...
.


Books

Pisier has authored several books and monographs in the fields of
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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...
,
harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...
, and
operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operato ...
. Among them are: * * * * * *


See also

* Pisier–Ringrose inequality


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