The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms

The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Author :
Publisher : American Mathematical Soc.
Total Pages : 119
Release :
ISBN-10 : 9780821804742
ISBN-13 : 082180474X
Rating : 4/5 (74X Downloads)

Book Synopsis The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms by : Gilles Pisier

Download or read book The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1996 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recently developed duality theory of operator spaces, bounded operators are replaced by 'completely bounded' ones, isomorphism 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 [italic capital]B([italic capital]H) (with H being Hilbert). One of the main results is the observation that there is a central object in this class: there is a unique self dual Hilbertian operator space (which we denote by [italic capitals]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.


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