In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) 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 ...
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In the recently developed duality theory of operator spaces (as developed by Effros-Ruan and Blecher-Paulsen) 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.
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Add this copy of Operator Hilbert Space Oh, Complex Interpolation and to cart. $19.08, good condition, Sold by ThriftBooks-Dallas rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 2006 by American Mathematical Society(RI).
Add this copy of The Operator Hilbert Space Oh, Complex Interpolation to cart. $65.44, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1996 by Amer Mathematical Society.
