Pisier, Gilles

Operator spaces and similarity problems

Doc. Math. (Bielefeld) Extra Vol. ICM Berlin 1998, Vol. I, 429-452 (1998)


We present an overview of the theory of "Operator Spaces" (sometimes called "non-commutative Banach spaces"), recently developed by Effros, Ruan, Blecher, Paulsen and others. We describe several applications of this new ideology to operator algebras and to various similarity problems.

Mathematics Subject Classification

46L05, 47L05, 46M05, 46B70


operator algebra, completely bounded, similar to contraction, uniform algebra, amenable group, operator space, non-commutative Banach spaces