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Author: Kenneth R. Davidson
Publisher: American Mathematical Soc.
ISBN: 147042309X
Category : Mathematics
Languages : en
Pages : 110
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Book Description
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: Kenneth R. Davidson
Publisher: American Mathematical Soc.
ISBN: 147042309X
Category : Mathematics
Languages : en
Pages : 110
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Book Description
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: Elias G. Katsoulis
Publisher: American Mathematical Soc.
ISBN: 1470435454
Category : C*-algebras
Languages : en
Pages : 85
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Book Description
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.
Author: Kenneth R. Davidson
Publisher: American Mathematical Soc.
ISBN: 0821853023
Category : Mathematics
Languages : en
Pages : 68
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Book Description
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.
Author: Hari Bercovici
Publisher: CRC Press
ISBN: 1351643037
Category : Mathematics
Languages : en
Pages : 219
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Book Description
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.
Author: Thierry Giordano
Publisher: Springer
ISBN: 3319708694
Category : Mathematics
Languages : en
Pages : 494
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Book Description
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 attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
Author: Peter A. Fillmore
Publisher: American Mathematical Soc.
ISBN: 0821805223
Category : Mathematics
Languages : en
Pages : 335
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Book Description
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 programme year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the programme. Topics covered include the classification of amenable C ]*-algebras, the Baum-Connes conjecture, E [0 semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Author: Ramon Antoine
Publisher: American Mathematical Soc.
ISBN: 1470427974
Category : Mathematics
Languages : en
Pages : 206
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Book Description
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.
Author: Aristides Katavolos
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 490
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Book Description
The proceedings of the August 1996 conference contain the 15 contributions of the main speakers. Themes include operator spaces; abstract operator algebras and their Hilbert modules; interaction with ring theory; non-self-adjoint operator algebras (limit algebras, reflexive algebras and subspaces, relations to basis theory); C*- algebraic quantum groups; endomorphisms of operator algebras, conditional expectations and projection maps; and applications, particularly to wavelet theory. A special lecture given by Stelios Negrepontis on the Pythagoreans is also presented. Annotation copyrighted by Book News, Inc., Portland, OR
Author: KADISON
Publisher: Springer Science & Business Media
ISBN: 1461229685
Category : Mathematics
Languages : en
Pages : 599
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Book Description
These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.
Author: Richard V. Kadison
Publisher: American Mathematical Soc.
ISBN: 9780821814413
Category : Mathematics
Languages : en
Pages : 798
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Book Description
