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.
Download or read book Complex Interpolation between Hilbert Banach and Operator Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 2010-10-07 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Tensor Products of C algebras and Operator Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2020-02-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Download or read book Mixed Norm Inequalities and Operator Space L p Embedding Theory written by Marius Junge and published by American Mathematical Soc.. This book was released on 2010 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.
Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces
Download or read book Completely Bounded Maps and Operator Algebras written by Vern Paulsen and published by Cambridge University Press. This book was released on 2002 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Quantum Functional Analysis written by Aleksandr I︠A︡kovlevich Khelemskiĭ and published by American Mathematical Soc.. This book was released on 2010 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1995-09 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Analysis written by Jim Agler and published by Cambridge University Press. This book was released on 2020-03-26 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Download or read book Quantum Potential Theory written by Philippe Biane and published by Springer Science & Business Media. This book was released on 2008-09-23 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Download or read book Operator Theory in Harmonic and Non commutative Analysis written by Joseph A. Ball and published by Springer. This book was released on 2014-06-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 23rd International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012. It includes twelve articles presenting both surveys of current research in operator theory and original results.
Download or read book Operator Algebras and Mathematical Physics written by Tirthankar Bhattacharyya and published by Birkhäuser. This book was released on 2015-09-29 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.
Download or read book Singular Integrals in Quantum Euclidean Spaces written by Adrían M. González-Pérez and published by American Mathematical Society. This book was released on 2021-11-16 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Operator Algebras Quantization and Noncommutative Geometry written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2004 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone. Papers range from expository and refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among Also featured is a reprint of P.R. Halmos's The Legend of John von Neumann. The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Download or read book Focus on Group Theory Research written by Lawrence M. Ying and published by Nova Publishers. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great many of the objects investigated in mathematics turn out to be groups. These include familiar number systems, such as the integers, the rational numbers, the real numbers, and the complex numbers under addition, as well as the non-zero rationals, reals, and complex numbers, under multiplication. Another important example is given by non-singular matrices under multiplication, and more generally, invertible functions under composition. Group theory allows for the properties of these systems and many others to be investigated in a more general setting, and its results are widely applicable. Group theory is also a rich source of theorems in its own right. Groups underlie many other algebraic structures such as fields and vector spaces. They are also important tools for studying symmetry in all its forms; the principle that the symmetries of any object form a group is foundational for much mathematics. For these reasons, group theory is an important area in modern mathematics, and also one with many applications to mathematical physics. This book presents the latest research in the field.
