Title: Operator Spaces and Similarity Problems

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.

1991 Mathematics Subject Classification: 46L05, 47D15, 46M05, 46B70

Keywords and Phrases: Operator space, operator algebra, completely bounded, similar to a contraction, uniform algebra, amenable group

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