Author: Gilles Pisier
Publisher: American Mathematical Soc.
ISBN: 082180474X
Category : Mathematics
Languages : en
Pages : 119
Book Description
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.
The Operator Hilbert Space $OH$, Complex Interpolation and Tensor Norms
Complex Interpolation between Hilbert, Banach and Operator Spaces
Author: Gilles Pisier
Publisher: American Mathematical Soc.
ISBN: 0821848429
Category : Mathematics
Languages : en
Pages : 92
Book Description
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).
Publisher: American Mathematical Soc.
ISBN: 0821848429
Category : Mathematics
Languages : en
Pages : 92
Book Description
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).
Tensor Products of C*-algebras and Operator Spaces
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1108479014
Category : Mathematics
Languages : en
Pages : 495
Book Description
Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Publisher: Cambridge University Press
ISBN: 1108479014
Category : Mathematics
Languages : en
Pages : 495
Book Description
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
Author: Marius Junge
Publisher: American Mathematical Soc.
ISBN: 0821846558
Category : Mathematics
Languages : en
Pages : 168
Book Description
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.
Publisher: American Mathematical Soc.
ISBN: 0821846558
Category : Mathematics
Languages : en
Pages : 168
Book Description
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.
Handbook of the Geometry of Banach Spaces
Author:
Publisher: Elsevier
ISBN: 0080533507
Category : Mathematics
Languages : en
Pages : 873
Book Description
Handbook of the Geometry of Banach Spaces
Publisher: Elsevier
ISBN: 0080533507
Category : Mathematics
Languages : en
Pages : 873
Book Description
Handbook of the Geometry of Banach Spaces
Completely Bounded Maps and Operator Algebras
Author: Vern Paulsen
Publisher: Cambridge University Press
ISBN: 9780521816694
Category : Mathematics
Languages : en
Pages : 316
Book Description
Table of contents
Publisher: Cambridge University Press
ISBN: 9780521816694
Category : Mathematics
Languages : en
Pages : 316
Book Description
Table of contents
Quantum Functional Analysis
Author: Aleksandr I︠A︡kovlevich Khelemskiĭ
Publisher: American Mathematical Soc.
ISBN: 082185254X
Category : Mathematics
Languages : en
Pages : 264
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 082185254X
Category : Mathematics
Languages : en
Pages : 264
Book Description
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.
Canadian Mathematical Bulletin
Operator Analysis
Author: Jim Agler
Publisher: Cambridge University Press
ISBN: 1108485448
Category : Mathematics
Languages : en
Pages : 393
Book Description
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.
Publisher: Cambridge University Press
ISBN: 1108485448
Category : Mathematics
Languages : en
Pages : 393
Book Description
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.
Introduction to Operator Space Theory
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 9780521811651
Category : Mathematics
Languages : en
Pages : 492
Book Description
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Publisher: Cambridge University Press
ISBN: 9780521811651
Category : Mathematics
Languages : en
Pages : 492
Book Description
An introduction to the theory of operator spaces, emphasising applications to C*-algebras.