The Operator Hilbert Space Oh Complex Interpolation And Tensor Norms
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Author | : Gilles Pisier |
Publisher | : American Mathematical Soc. |
Total Pages | : 119 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 082180474X |
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.
Author | : Gilles Pisier |
Publisher | : American Mathematical Soc. |
Total Pages | : 92 |
Release | : 2010-10-07 |
Genre | : Mathematics |
ISBN | : 0821848429 |
Motivated by a question of Vincent Lafforgue, the author studies the Banach spaces $X$ satisfying the following property: there is a function $\varepsilon\to \Delta_X(\varepsilon)$ tending to zero with $\varepsilon>0$ such that every operator $T\colon \ L_2\to L_2$ with $\T\\le \varepsilon$ that is simultaneously contractive (i.e., of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\varepsilon)$ on $L_2(X)$. The author shows that $\Delta_X(\varepsilon) \in O(\varepsilon^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $\theta>0$ (see Corollary 6.7), where $\theta$-Hilbertian is meant in a slightly more general sense than in the author's earlier paper (1979).
Author | : Gilles Pisier |
Publisher | : Cambridge University Press |
Total Pages | : 495 |
Release | : 2020-02-27 |
Genre | : Mathematics |
ISBN | : 1108479014 |
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Author | : Marius Junge |
Publisher | : American Mathematical Soc. |
Total Pages | : 168 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821846558 |
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.
Author | : |
Publisher | : Elsevier |
Total Pages | : 873 |
Release | : 2003-05-06 |
Genre | : Mathematics |
ISBN | : 0080533507 |
Handbook of the Geometry of Banach Spaces
Author | : Vern Paulsen |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780521816694 |
Author | : Aleksandr I︠A︡kovlevich Khelemskiĭ |
Publisher | : American Mathematical Soc. |
Total Pages | : 264 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 082185254X |
Interpreting ""quantized coefficients"" as finite rank operators in a fixed Hilbert space allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject.
Author | : |
Publisher | : |
Total Pages | : 128 |
Release | : 1995-09 |
Genre | : |
ISBN | : |
Author | : Jim Agler |
Publisher | : Cambridge University Press |
Total Pages | : 393 |
Release | : 2020-03-26 |
Genre | : Mathematics |
ISBN | : 1108485448 |
This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.
Author | : Gilles Pisier |
Publisher | : Cambridge University Press |
Total Pages | : 492 |
Release | : 2003-08-25 |
Genre | : Mathematics |
ISBN | : 9780521811651 |
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.