# Gilles Pisier

**Gilles I. Pisier** (born 18 November 1950) is a professor of mathematics at the Pierre and Marie Curie University and a distinguished professor and A.G. and M.E. Owen Chair of Mathematics at the Texas A&M University.^{[1]}^{[2]} He is known for his contributions to several fields of mathematics, including functional analysis, probability theory, harmonic analysis, and operator theory. He has also made fundamental contributions to the theory of C*-algebras.^{[3]} Gilles is the younger brother of French actress Marie-France Pisier.

Gilles Pisier | |
---|---|

Born | |

Nationality | French |

Alma mater | Paris Diderot University |

Known for | Contributions to functional analysis, probability theory, harmonic analysis, operator theory |

Awards | Ostrowski Prize (1997) Salem Prize (1979) |

Scientific career | |

Fields | Mathematics |

Institutions | Pierre and Marie Curie University, Texas A&M University |

Doctoral advisor | Laurent Schwartz |

## ResearchEdit

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

### Geometry of Banach spacesEdit

In the "local theory of Banach spaces", Pisier and Bernard Maurey developed the theory of Rademacher type, following its use in probability theory by J. Hoffman–Jorgensen and in the characterization of Hilbert spaces among Banach spaces by S. Kwapień. Using probability in vector spaces, Pisier proved that super-reflexive Banach spaces can be renormed with the modulus of uniform convexity having "power type".^{[4]}^{[5]} His work (with Per Enflo and Joram Lindenstrauss) on the "three–space problem" influenced the work on quasi–normed spaces by Nigel Kalton.

### Operator theoryEdit

Pisier transformed the area of operator spaces. In the 1990s, he solved two long-standing open problems. In the theory of C*-algebras, he solved, jointly with Marius Junge, the problem of the uniqueness of C* -norms on the tensor product of two copies of *B(H)*, the bounded linear operators on a Hilbert space *H*. He and Junge were able to produce two such tensor norms that are nonequivalent.^{[3]} In 1997, he constructed an operator that was polynomially bounded but not similar to a contraction, answering a famous question of Paul Halmos.

## AwardsEdit

He was an invited speaker at the 1983 ICM^{[6]} and
a plenary speaker at the 1998 ICM.^{[7]}^{[8]} 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.^{[9]} In 2012 he became a fellow of the American Mathematical Society.^{[10]}

## BooksEdit

Pisier has authored several books and monographs in the fields of functional analysis, harmonic analysis, and operator theory. Among them are:

- "The Volume of Convex Bodies and Banach Space Geometry", Cambridge University Press, 2nd ed., 1999. First published in 1989.
^{[11]} - "Introduction to Operator Space Theory", Cambridge University Press, 2003.
- "The Operator Hilbert Space OH, Complex Interpolation and Tensor Norms", Amer Mathematical Society, 1996.
- "Factorization of Linear Operators and Geometry of Banach Spaces", Amer Mathematical Society, 1986.
- "Similarity Problems and Completely Bounded Maps", Springer, 2nd ed., 2001. First published in 1995.
- "Random Fourier Series with Applications to Harmonic Analysis", with Michael B. Marcus, Princeton University Press, 1981.
^{[12]}

## ReferencesEdit

**^**"Gilles Pisier". Retrieved 14 April 2010.**^**"Gilles Pisier". Texas A&M University. Retrieved 5 March 2010.- ^
^{a}^{b}"Nesterenko and Pisier Share Ostrowski Prize" (PDF). American Mathematical Society. August 1998. Retrieved 5 March 2010. **^**Beauzamy, Bernard (1985) [1982].*Introduction to Banach Spaces and their Geometry*(Second revised ed.). North-Holland. ISBN 0-444-86416-4. MR 0889253.**^**Pisier, Gilles (1975). "Martingales with values in uniformly convex spaces".*Israel Journal of Mathematics*.**20**(3–4): 326–350. doi:10.1007/BF02760337. MR 0394135.**^**Pisier, Gilles (1983). "Finite Rank Projections on Banach Spaces and a Conjecture of Grothendieck" (PDF).*Proceedings of the ICM, 1983*. pp. 1027–1039.**^**"ICM Plenary and Invited Speakers".*mathunion.org*.**^**Pisier, Gilles (1998). "Operator spaces and similarity problems".*Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I*. pp. 429–452.**^**"UCLA Distinguished Lecturers". University of California. Retrieved 13 March 2010.**^**List of Fellows of the American Mathematical Society, retrieved 2013-05-05.**^**Burkholder, Donald L. (1991). "Review:*The Volume of Convex Bodies and Banach Space Geometry*, by G. Pisier".*Bulletin of the American Mathematical Society*.**25**(1): 140–145. doi:10.1090/s0273-0979-1991-16046-5.**^**Rider, Daniel (1983). "Review:*Random Fourier Series with Applications to Harmonic Analysis*, by M. B. Marcus and G. Pisier".*Bulletin of the American Mathematical Society*.**8**(2): 353–356. doi:10.1090/s0273-0979-1983-15119-4.