The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Author | : Gilles Pisier |
Publisher | : American Mathematical Soc. |
Total Pages | : 119 |
Release | : 1996 |
ISBN-10 | : 9780821804742 |
ISBN-13 | : 082180474X |
Rating | : 4/5 (74X Downloads) |
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.