Gilles Pisier
Visit: November 4 - November 11

Seminar : November 6, 2001, 1:00 p.m. in MS 6627
Colloquium : November 8, 2001, 4:00 p.m. in MS 6627

Seminar Title : Grothendieck's Theorem for Operator Spaces
Abstract :

The original Grothendieck Theorem is a factorization theorem for bounded bilinear forms on -spaces, or similar function spaces. The talk will discuss the recent generalization of this theorem proved for "completely bounded" bilinear forms on C^*-algebras (or on more general operator spaces) in recent joint work with D. Shlyakhtenko. The notion of "exact" operator space plays a central role in this result.

Colloquium Title : High Dimensional Operator Space Theory
Abstract :

The theory of "operator spaces" (or non-commutative Banach spaces) was recently developed intensively by Effros-Ruan, Blecher-Paulsen, and others after them. In this talk we will concentrate on the finite dimensional (often called "local") aspects of that theory. We will focus our attention on the metric space of all n-dimensional operator spaces, equipped with the completely bounded analogue of the Banach-Mazur distance. We will explain why this space is not separable for n > 2, in sharp contrast with the Banach-Mazur case, and how this implies the existence of two distinct C^*-tensor products of B(l₂ ) with itself. The best related known estimates use certain expanders known as "Ramanujan" graphs. We will also estimate how a general n-dimensional operator space can be approximated by Hilbertian operator spaces, in connection with the notion of "exactness".

Gilles Pisier is a renowned leader in the area of functional analysis. Many of his solutions are classic in the area of Banach space theory. He holds the Owen chair of mathematics at Texas A & M and he is also a professor at Paris VI. Pisier's interests include Functional Analysis, Probability, Harmonic Analysis, Operator theory, and C*-algebras.

Pisier was a plenary speaker at the ICM Congress in Berlin in 1998. In addition, he was a primary speaker in the Functional Analysis Section of the 1983 ICM Congress in Warsaw, Poland.

Over the years Pisier's exceptional achievements have been recognized by many prizes and distinctions, such as the Ostrowski Prize 1997, Grands Prix de l'Academie des Sciences de Paris 1992, and Salem Prize 1979. He has been a "Membre Correspondent de l'Academie Francaise'' since 1994.