Semicrossed Products Of Operator Algebras By Semigroups
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Semicrossed Products Of Operator Algebras By Semigroups
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Author : Kenneth R. Davidson
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
Semicrossed Products Of Operator Algebras By Semigroups written by Kenneth R. Davidson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-25 with Mathematics categories.
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.
Crossed Products Of Operator Algebras
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Author : Elias G. Katsoulis
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-10
Crossed Products Of Operator Algebras written by Elias G. Katsoulis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
Recent Advances In Operator Theory And Operator Algebras
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Author : Hari Bercovici
language : en
Publisher: CRC Press
Release Date : 2017-08-07
Recent Advances In Operator Theory And Operator Algebras written by Hari Bercovici and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.
This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.
Functional Analysis And Operator Algebras
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Author : Kenneth R. Davidson
language : en
Publisher: Springer Nature
Release Date : 2025-05-11
Functional Analysis And Operator Algebras written by Kenneth R. Davidson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-11 with Mathematics categories.
This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include $H^p$ spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.
Crossed Products Of C Algebras Topological Dynamics And Classification
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Author : Thierry Giordano
language : en
Publisher: Springer
Release Date : 2018-08-28
Crossed Products Of C Algebras Topological Dynamics And Classification written by Thierry Giordano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-28 with Mathematics categories.
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attentionto the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Tensor Products And Regularity Properties Of Cuntz Semigroups
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Author : Ramon Antoine
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-23
Tensor Products And Regularity Properties Of Cuntz Semigroups written by Ramon Antoine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
The Cuntz semigroup of a -algebra is an important invariant in the structure and classification theory of -algebras. It captures more information than -theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a -algebra , its (concrete) Cuntz semigroup is an object in the category of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter -semigroups. The authors establish the existence of tensor products in the category and study the basic properties of this construction. They show that is a symmetric, monoidal category and relate with for certain classes of -algebras. As a main tool for their approach the authors introduce the category of pre-completed Cuntz semigroups. They show that is a full, reflective subcategory of . One can then easily deduce properties of from respective properties of , for example the existence of tensor products and inductive limits. The advantage is that constructions in are much easier since the objects are purely algebraic.
Operator Algebras For Multivariable Dynamics
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Author : Kenneth R. Davidson
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Operator Algebras For Multivariable Dynamics written by Kenneth R. Davidson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.
Crossed Products By Hecke Pairs
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Author : Rui Palma
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-19
Crossed Products By Hecke Pairs written by Rui Palma and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
The author develops a theory of crossed products by actions of Hecke pairs , motivated by applications in non-abelian -duality. His approach gives back the usual crossed product construction whenever is a group and retains many of the aspects of crossed products by groups. The author starts by laying the -algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different -completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.
Boundary Conditions And Subelliptic Estimates For Geometric Kramers Fokker Planck Operators On Manifolds With Boundaries
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Author : Francis Nier
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-19
Boundary Conditions And Subelliptic Estimates For Geometric Kramers Fokker Planck Operators On Manifolds With Boundaries written by Francis Nier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.
This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.
Fundamental Solutions And Local Solvability For Nonsmooth Hormander S Operators
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Author : Marco Bramanti
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25
Fundamental Solutions And Local Solvability For Nonsmooth Hormander S Operators written by Marco Bramanti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Mathematics categories.
The authors consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that also possesses second derivatives, and they deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . The authors also prove estimates on this solution.