The Operator Hilbert Space Oh Complex Interpolation And Tensor Norms
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The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Author: Gilles Pisier
language: en
Publisher: American Mathematical Soc.
Release Date: 1996
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.
Tensor Products of C*-algebras and Operator Spaces
Author: Gilles Pisier
language: en
Publisher: Cambridge University Press
Release Date: 2020-02-27
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.