Hilbert C Modules And Quantum Markov Semigroups

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Hilbert C*- Modules and Quantum Markov Semigroups

Author : Lunchuan Zhang
Publisher : Springer
ISBN 13 : 9789819986675
Total Pages : 0 pages
Book Rating : 4.9/5 (866 download)

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Book Synopsis Hilbert C*- Modules and Quantum Markov Semigroups by : Lunchuan Zhang

Download or read book Hilbert C*- Modules and Quantum Markov Semigroups written by Lunchuan Zhang and published by Springer. This book was released on 2024-02-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the basic theory of Hilbert C*-module in detail, covering a wide range of applications from generalized index to module framework. At the center of the book, the Beurling-Deny criterion is characterized between operator valued Dirichlet forms and quantum Markov semigroups, hence opening a new field of quantum probability research. The general scope of the book includes: basic theory of Hilbert C*-modules; generalized indices and module frames; operator valued Dirichlet forms; and quantum Markov semigroups. This book will be of value to scholars and graduate students in the fields of operator algebra, quantum probability and quantum information.

Hilbert C*- Modules and Quantum Markov Semigroups

Author : Lunchuan Zhang
Publisher : Springer Nature
ISBN 13 : 9819986680
Total Pages : 222 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Hilbert C*- Modules and Quantum Markov Semigroups by : Lunchuan Zhang

Download or read book Hilbert C*- Modules and Quantum Markov Semigroups written by Lunchuan Zhang and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Independent Increment Processes I

Author : David Applebaum
Publisher : Springer
ISBN 13 : 3540314504
Total Pages : 312 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Quantum Independent Increment Processes I by : David Applebaum

Download or read book Quantum Independent Increment Processes I written by David Applebaum and published by Springer. This book was released on 2005-09-12 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Classification of $E_0$-Semigroups by Product Systems

Author : Michael Skeide
Publisher : American Mathematical Soc.
ISBN 13 : 1470417383
Total Pages : 138 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 138 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.

Quantum Probability and Related Topics

Author : J. C. Garc¡a
Publisher : World Scientific
ISBN 13 : 9812835261
Total Pages : 288 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Quantum Probability and Related Topics by : J. C. Garc¡a

Download or read book Quantum Probability and Related Topics written by J. C. Garc¡a and published by World Scientific. This book was released on 2008 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume contains recent results in quantum probability and related topics. The contributions include peer-reviewed papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, applications of quantum probability in physics, and quantum and classical models in biology. This diversity reflects the strong and constructive relations between quantum probability and different sectors of mathematics, physics, and other sciences and technologies."--BOOK JACKET.

Quantum Probability And Related Topics - Proceedings Of The 28th Conference

Author : Roberto Quezada
Publisher : World Scientific
ISBN 13 : 9814469769
Total Pages : 288 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Probability And Related Topics - Proceedings Of The 28th Conference by : Roberto Quezada

Download or read book Quantum Probability And Related Topics - Proceedings Of The 28th Conference written by Roberto Quezada and published by World Scientific. This book was released on 2008-10-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains recent results in quantum probability and related topics. The contributions include peer-reviewed papers on interacting Fock space and orthogonal polynomials, quantum Markov semigroups, infinitely divisible processes, free probability, white noise, quantum filtering and control, quantum information, dilations, applications of quantum probability in physics, and quantum and classical models in biology. This diversity reflects the strong and constructive relations between quantum probability and different sectors of mathematics, physics, and other sciences and technologies.

Hilbert C*-modules

Author : Vladimir Markovich Manuĭlov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889664
Total Pages : 216 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Hilbert C*-modules by : Vladimir Markovich Manuĭlov

Download or read book Hilbert C*-modules written by Vladimir Markovich Manuĭlov and published by American Mathematical Soc.. This book was released on with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C*$-modules. Hilbert $C*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C $ is replaced by an arbitrary $C*$-algebra. The general theory of Hilbert $C*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool inoperator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of thetheory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis

Author : Wolfgang Freudenberg
Publisher : World Scientific
ISBN 13 : 9812382887
Total Pages : 277 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis by : Wolfgang Freudenberg

Download or read book Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis written by Wolfgang Freudenberg and published by World Scientific. This book was released on 2003 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, the stochastic limit, quantum teleportation and other areas. Contents: Markov Property -- Recent Developments on the Quantum Markov Property (L Accardi & F Fidaleo); Stationary Quantum Stochastic Processes from the Cohomological Point of View (G G Amosov); The Feller Property of a Class of Quantum Markov Semigroups II (R Carbone & F Fagnola); Recognition and Teleportation (K-H Fichtner et al.); Prediction Errors and Completely Positive Maps (R Gohm); Multiplicative Properties of Double Stochastic Product Integrals (R L Hudson); Isometric Cocycles Related to Beam Splittings (V Liebscher); Multiplicativity via a Hat Trick (J M Lindsay & S J Wills); Dilation Theory and Continuous Tensor Product Systems of Hilbert Modules (M Skeide); Quasi-Free Fermion Planar Quantum Stochastic Integrals (W J Spring & I F Wilde); and other papers.

Quantum Probability And Related Topics - Proceedings Of The 30th Conference

Author : Rolando Rebolledo
Publisher : World Scientific
ISBN 13 : 9814462179
Total Pages : 339 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Probability And Related Topics - Proceedings Of The 30th Conference by : Rolando Rebolledo

Download or read book Quantum Probability And Related Topics - Proceedings Of The 30th Conference written by Rolando Rebolledo and published by World Scientific. This book was released on 2011-01-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.

Operator Theory, Functional Analysis and Applications

Author : M. Amélia Bastos
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.

Proceedings of the First International Forum on Financial Mathematics and Financial Technology

Author : Zhiyong Zheng
Publisher : Springer Nature
ISBN 13 : 9811583730
Total Pages : 238 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Proceedings of the First International Forum on Financial Mathematics and Financial Technology by : Zhiyong Zheng

Download or read book Proceedings of the First International Forum on Financial Mathematics and Financial Technology written by Zhiyong Zheng and published by Springer Nature. This book was released on 2021-02-08 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.

Quantum Stochastic Processes and Noncommutative Geometry

Author : Kalyan B. Sinha
Publisher : Cambridge University Press
ISBN 13 : 1139461699
Total Pages : 301 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Quantum Stochastic Processes and Noncommutative Geometry by : Kalyan B. Sinha

Download or read book Quantum Stochastic Processes and Noncommutative Geometry written by Kalyan B. Sinha and published by Cambridge University Press. This book was released on 2007-01-25 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.

Hilbert C*-modules

Author : Vladimir Markovich Manuĭlov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838105
Total Pages : 202 pages
Book Rating : 4.8/5 (381 download)

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Book Synopsis Hilbert C*-modules by : Vladimir Markovich Manuĭlov

Download or read book Hilbert C*-modules written by Vladimir Markovich Manuĭlov and published by American Mathematical Soc.. This book was released on 2005 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert $C^*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C}$ is replaced by an arbitrary $C^*$-algebra. The general theory of Hilbert $C^*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, in index theory of elliptic operators, in $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C^*$-modules is interesting on its own. The present book is an introduction to the theory of Hilbert $C^*$-modules. The authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

Stochastics in Finite and Infinite Dimensions

Author : Takeyuki Hida
Publisher : Springer Science & Business Media
ISBN 13 : 1461201675
Total Pages : 436 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastics in Finite and Infinite Dimensions by : Takeyuki Hida

Download or read book Stochastics in Finite and Infinite Dimensions written by Takeyuki Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.

Quantum Probability And Infinite-dimensional Analysis: Proceedings Of The Conference

Author : Wolfgang Freudenberg
Publisher : World Scientific
ISBN 13 : 9814486566
Total Pages : 277 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Probability And Infinite-dimensional Analysis: Proceedings Of The Conference by : Wolfgang Freudenberg

Download or read book Quantum Probability And Infinite-dimensional Analysis: Proceedings Of The Conference written by Wolfgang Freudenberg and published by World Scientific. This book was released on 2003-01-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, quantum Markov processes, the stochastic limit, quantum teleportation and other areas.

Quantum Potential Theory

Author : Philippe Biane
Publisher : Springer
ISBN 13 : 3540693653
Total Pages : 467 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Quantum Potential Theory by : Philippe Biane

Download or read book Quantum Potential Theory written by Philippe Biane and published by Springer. This book was released on 2008-10-16 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.

Advances in Quantum Dynamics

Author : Geoffrey L. Price
Publisher : American Mathematical Soc.
ISBN 13 : 0821832158
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advances in Quantum Dynamics by : Geoffrey L. Price

Download or read book Advances in Quantum Dynamics written by Geoffrey L. Price and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversiblesystems, also called dissipative systems. The time parameter is the half-line, and the transformations are now endomorphisms as opposed to automorphisms. For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such asBrownian motion, dilation theory, quantum probability, and free probability. The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.