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.
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.
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.
Download or read book Problems in the Classification of E0 semigroups written by Masayasu Aotani and published by . This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Random Sets and Invariants for Type II Continuous Tensor Product Systems of Hilbert Spaces written by Volkmar Liebscher and published by American Mathematical Soc.. This book was released on 2009-04-10 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Semicrossed Products of Operator Algebras by Semigroups written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantization Nonlinear Partial Differential Equations and Operator Algebra written by William Arveson and published by American Mathematical Soc.. This book was released on 1996 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Continuous Analogues of Fock Space written by William Arveson and published by American Mathematical Soc.. This book was released on 1989 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of classifying semigroups of endomorphisms of type [italic]I[subscript]infinity symbol factors to outer conjugacy is reduced to the problem of classifying certain simpler structures associated to them, called product systems. Product systems are intimately connected with continuous tensor products of Hilbert spaces. We develop the general theory of product systems and give a number of applications to semigroups of endomorphisms of von Neumann algebras; in particular, we introduce a numerical invariant for such semigroups which is analogous to the Fredholm index.
Download or read book Quantum Stochastics and Information written by V. P. Belavkin and published by World Scientific. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Stochastics and Information written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topologically Protected States in One Dimensional Systems written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book The abc Problem for Gabor Systems written by Xin-Rong Dai and published by American Mathematical Soc.. This book was released on 2016-10-05 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Locally Analytic Vectors in Representations of Locally adic Analytic Groups written by Matthew J. Emerton and published by American Mathematical Soc.. This book was released on 2017-07-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.
Download or read book Oseledec Multiplicative Ergodic Theorem for Laminations written by Viêt-Anh Nguyên and published by American Mathematical Soc.. This book was released on 2017-02-20 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a -dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank , where and are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained. The main ingredients of the author's method are the theory of Brownian motion, the analysis of the heat diffusions on Riemannian manifolds, the ergodic theory in discrete dynamics and a geometric study of laminations.
Download or read book Igusa s p Adic Local Zeta Function and the Monodromy Conjecture for Non Degenerate Surface Singularities written by Bart Bories and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerate surface singularity. The authors start from their work and obtain the same result for Igusa's p-adic and the motivic zeta function. In the p-adic case, this is, for a polynomial f∈Z[x,y,z] satisfying f(0,0,0)=0 and non-degenerate with respect to its Newton polyhedron, we show that every pole of the local p-adic zeta function of f induces an eigenvalue of the local monodromy of f at some point of f−1(0)⊂C3 close to the origin. Essentially the entire paper is dedicated to proving that, for f as above, certain candidate poles of Igusa's p-adic zeta function of f, arising from so-called B1-facets of the Newton polyhedron of f, are actually not poles. This turns out to be much harder than in the topological setting. The combinatorial proof is preceded by a study of the integral points in three-dimensional fundamental parallelepipeds. Together with the work of Lemahieu and Van Proeyen, this main result leads to the Monodromy Conjecture for the p-adic and motivic zeta function of a non-degenerate surface singularity.
