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Operator spaces. (English) Zbl 1041.46042
Johnson, W. B. (ed.) et al., Handbook of the geometry of Banach spaces. Volume 2. Amsterdam: North-Holland (ISBN 0-444-51305-1/hbk). 1425-1458 (2003).
This is a deep yet very readable guide to operator spaces, by one of the leading experts in the field. Topics discussed in the article include: tensor products of operator spaces and \(C^*\)-algebras; Ruan’s characterization of operator spaces in terms of matricial norms; local theory of operator spaces; non-commutative \(L_p\)-spaces; exactness and local reflexivity; duality, quotients, ultraproducts, and interpolation of operator spaces; injective and projective operator spaces. Most proofs are omitted, but references to articles and books containing them are given. The paper contains an extensive bibliography.
For the entire collection see [Zbl 1013.46001].

46L07 Operator spaces and completely bounded maps
46L52 Noncommutative function spaces
46-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functional analysis
operator spaces