Classification Of E 0 Semigroups By Product Systems

Author : Michael Skeide
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 46,6 Mb
Release : 2016-03-10
Category : Endomorphisms (Group theory)
ISBN : 9781470417383

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Classification of $E_0$-Semigroups by Product Systems by Michael Skeide Pdf

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.

Author : Geoffrey L. Price
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 47,5 Mb
Release : 2003
Category : Quantum theory
ISBN : 9780821832158

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Advances in Quantum Dynamics by Geoffrey L. Price Pdf

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.

Author : William Arveson
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 48,5 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9780387215242

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Noncommutative Dynamics and E-Semigroups by William Arveson Pdf

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.

Author : Masayasu Aotani
Publisher : Unknown
Page : 378 pages
File Size : 53,5 Mb
Release : 1996
Category : Electronic
ISBN : UCAL:C3389674

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Problems in the Classification of E0-semigroups by Masayasu Aotani Pdf

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 42,6 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

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Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

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.

Author : Volkmar Liebscher
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 40,9 Mb
Release : 2009-04-10
Category : Mathematics
ISBN : 9780821843185

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Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces by Volkmar Liebscher Pdf

In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.

Author : Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 44,8 Mb
Release : 2017-04-25
Category : Operator algebras
ISBN : 9781470423094

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Semicrossed Products of Operator Algebras by Semigroups by Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis Pdf

The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Author : William Arveson,Thomas Branson,Irving Ezra Segal
Publisher : American Mathematical Soc.
Page : 239 pages
File Size : 53,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821803813

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Quantization, Nonlinear Partial Differential Equations, and Operator Algebra by William Arveson,Thomas Branson,Irving Ezra Segal Pdf

This book describes the outstanding recent progress in this important and challenging field and presents general background for the scientific context and specifics regarding key difficulties. Quantization is developed in the context of rigorous nonlinear quantum field theory in four dimensions and in connection with symplectic manifold theory and random Schrödinger operators. Nonlinear wave equations are exposed in relation to recent important progress in general relativity, in purely mathematical terms of microlocal analysis, and as represented by progress on the relativistic Boltzmann equation. Most of the developments in this volume appear in book form for the first time. The resulting work is a concise and informative way to explore the field and the spectrum of methods available for its investigation.

Author : William Arveson
Publisher : American Mathematical Soc.
Page : 66 pages
File Size : 55,7 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821824726

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Continuous Analogues of Fock Space by William Arveson Pdf

Author : V. P. Belavkin,M. Guta
Publisher : World Scientific
Page : 410 pages
File Size : 48,6 Mb
Release : 2008
Category : Science
ISBN : 9789812832962

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Quantum Stochastics and Information by V. P. Belavkin,M. Guta Pdf

Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems.This volume contains a selection of regular research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789814518284

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Quantum Stochastics and Information by Anonim Pdf

Author : Charles Fefferman,James P. Lee-Thorp,M. I. Weinstein
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 48,9 Mb
Release : 2017-04-25
Category : Dirac equation
ISBN : 9781470423230

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Topologically Protected States in One-Dimensional Systems by Charles Fefferman,James P. Lee-Thorp,M. I. Weinstein Pdf

The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.

Author : Joachim Zacharias
Publisher : American Mathematical Soc.
Page : 135 pages
File Size : 46,6 Mb
Release : 2000
Category : C*-algebras
ISBN : 9780821815458

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Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras by Joachim Zacharias Pdf

This book is intended for graduate students and research mathematicians interested in operator algebras

Author : Wolfgang Freudenberg
Publisher : World Scientific
Page : 277 pages
File Size : 42,6 Mb
Release : 2003
Category : Science
ISBN : 9789812382887

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Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis by Wolfgang Freudenberg Pdf

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.

Author : Xin-Rong Dai,Qiyu Sun
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 40,6 Mb
Release : 2016-10-05
Category : Gabor frames
ISBN : 9781470420154

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The $abc$-Problem for Gabor Systems by Xin-Rong Dai,Qiyu Sun Pdf

A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.