Memoirs of the American Mathematical Society 1996; 103 pp; softcover Volume: 122 ISBN10: 082180474X ISBN13: 9780821804742 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/122/585
 In the recently developed duality theory of operator spaces (as developed by EffrosRuan and BlecherPaulsen) bounded operators are replaced by completely bounded ones, isomorphisms by complete isomorphisms, and Banach spaces by operator spaces. This allows for distinguishing between the various ways in which a given Banach space can be embedded isometrically into \(B(H)\) (with \(H\) being Hilbert). In this new category, several operator spaces which are isomorphic (as Banach spaces) to a Hilbert space play an important role. For instance the row and column Hilbert spaces and several other examples appearing naturally in the construction of the Boson or Fermion Fock spaces have been studied extensively. One of the main results of this memoir is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (denoted by \(OH\) ) which seems to play the same central role in the category of operator spaces that Hilbert spaces play in the category of Banach spaces. This new concept, called "the operator Hilbert space" and denoted by \(OH\), is introduced and thoroughly studied in this volume. Readership Graduate students and research mathematicians interested in functional analysis. Table of Contents  Introduction
 The operator Hilbert space
 Complex interpolation
 The \(oh\) tensor product
 Weights on partially ordered vector spaces
 \((2,w)\)summing operators
 The gammanorms and their dual norms
 Operators factoring through \(OH\)
 Factorization through a Hilbertian operator space
 On the "local theory" of operator spaces
 Open questions
 References
