Dilations, Completely Positive Maps and Geometry

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Publisher : Springer
ISBN 13 : 9789819983513
Total Pages : 0 pages
Book Rating : 4.9/5 (835 download)

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Book Synopsis Dilations, Completely Positive Maps and Geometry by : B.V. Rajarama Bhat

Download or read book Dilations, Completely Positive Maps and Geometry written by B.V. Rajarama Bhat and published by Springer. This book was released on 2024-02-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently. A good portion of the book discusses various geometrical objects like the bidisc, the Euclidean unit ball, and the symmetrized bidisc. It shows the similarities and differences between the dilation theory in these domains. While completely positive maps play a big role in the dilation theory of the Euclidean unit ball, this is not so in the symmetrized bidisc for example. There, the central role is played by an operator equation. Targeted to graduate students and researchers, the book introduces the reader to different techniques applicable in different domains.

Completely Bounded Maps and Dilations

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Publisher :
ISBN 13 :
Total Pages : 214 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Completely Bounded Maps and Dilations by : Vern I. Paulsen

Download or read book Completely Bounded Maps and Dilations written by Vern I. Paulsen and published by . This book was released on 1986 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Algebras, Quantization, and Noncommutative Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821834029
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator Algebras, Quantization, and Noncommutative Geometry by : Robert S. Doran

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.

Operator Theory, Functional Analysis and Applications

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Publisher : Springer Nature
ISBN 13 : 3030519457
Total Pages : 654 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Operator Theory, Functional Analysis and Applications by : M. Amélia Bastos

Download or read book Operator Theory, Functional Analysis and Applications written by M. Amélia Bastos and published by Springer Nature. This book was released on 2021-03-31 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

Stochastic Processes, Physics and Geometry: New Interplays. II

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821819609
Total Pages : 650 pages
Book Rating : 4.8/5 (196 download)

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Book Synopsis Stochastic Processes, Physics and Geometry: New Interplays. II by : Sergio Albeverio

Download or read book Stochastic Processes, Physics and Geometry: New Interplays. II written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.

Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

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Publisher : American Mathematical Soc.
ISBN 13 : 1470434555
Total Pages : 104 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions by : J. William Helton

Download or read book Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions written by J. William Helton and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→K such that C=V∗TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor ϑ(d), expressed as a ratio of Γ functions for d even, of all d×d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.

Noncommutative Dynamics and E-Semigroups

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Publisher : Springer Science & Business Media
ISBN 13 : 0387215247
Total Pages : 442 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Noncommutative Dynamics and E-Semigroups by : William Arveson

Download or read book Noncommutative Dynamics and E-Semigroups written by William Arveson and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

Operator-Valued Measures, Dilations, and the Theory of Frames

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Publisher : American Mathematical Soc.
ISBN 13 : 0821891723
Total Pages : 84 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator-Valued Measures, Dilations, and the Theory of Frames by : Deguang Han

Download or read book Operator-Valued Measures, Dilations, and the Theory of Frames written by Deguang Han and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.

Classification of $E_0$-Semigroups by Product Systems

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Publisher : American Mathematical Soc.
ISBN 13 : 1470417383
Total Pages : 126 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Classification of $E_0$-Semigroups by Product Systems by : Michael Skeide

Download or read book Classification of $E_0$-Semigroups by Product Systems written by Michael Skeide and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.

Reality and Measurement in Algebraic Quantum Theory

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Publisher : Springer
ISBN 13 : 9811324875
Total Pages : 396 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Reality and Measurement in Algebraic Quantum Theory by : Masanao Ozawa

Download or read book Reality and Measurement in Algebraic Quantum Theory written by Masanao Ozawa and published by Springer. This book was released on 2018-11-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

Revista Matemática Iberoamericana

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Publisher :
ISBN 13 :
Total Pages : 772 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Revista Matemática Iberoamericana by :

Download or read book Revista Matemática Iberoamericana written by and published by . This book was released on 2011 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Algebras and Their Modules

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Publisher : Oxford University Press
ISBN 13 : 0191523569
Total Pages : pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Operator Algebras and Their Modules by : David P. Blecher

Download or read book Operator Algebras and Their Modules written by David P. Blecher and published by Oxford University Press. This book was released on 2004-10-07 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable reference is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area. A major trend in modern mathematics, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, nonselfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras, and their modules, naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important noncommutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a lengthy section of notes containing a wealth of additional information.

Dissertation Abstracts International

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Publisher :
ISBN 13 :
Total Pages : 810 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Dissertation Abstracts International by :

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2009 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Information and Computing

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Publisher : World Scientific
ISBN 13 : 9812774491
Total Pages : 398 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Quantum Information and Computing by : Luigi Accardi

Download or read book Quantum Information and Computing written by Luigi Accardi and published by World Scientific. This book was released on 2006 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of o-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum Logical Gates Realized by Beam Splittings (W Freudenberg et al.); Noncanonical Representations of a Multi-dimensional Brownian Motion (Y Hibino); Information, Innovation and Elemental Random Field (T Hida); Generalized Sectors and Adjunctions to Control MicroOCoMacro Transitions (I Ojima); Saturation of an Entropy Bound and Quantum Markov States (D Petz); An Infinite Dimensional Laplacian Acting on Some Class of L(r)vy White Noise Functionals (K Sait); Structure of Linear Processes (S Si & W W Htay); Group Theory of Dynamical Maps (E C G Sudarshan); Quantum Entanglement, Purification, and Linear-optics Quantum Gates with Photonic Qubits (P Walther & A Zeilinger); On Quantum Mutual Type Measures and Capacity (N Watanabe); and other papers. Readership: Researchers in quantum physics and theoretical physics."

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 796 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Dynamical Semigroups and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 354070860X
Total Pages : 138 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Quantum Dynamical Semigroups and Applications by : Robert Alicki

Download or read book Quantum Dynamical Semigroups and Applications written by Robert Alicki and published by Springer Science & Business Media. This book was released on 2007-04-23 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinvigorated by advances and insights the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. Originally published as Volume 286 (1987) in Lecture in Physics, this volume has been newly typeset, revised and corrected and also expanded to include a review on recent developments.

Completely Bounded Maps and Operator Algebras

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Publisher : Cambridge University Press
ISBN 13 : 9780521816694
Total Pages : 316 pages
Book Rating : 4.8/5 (166 download)

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Book Synopsis Completely Bounded Maps and Operator Algebras by : Vern Paulsen

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