Download or read book C semigroup Bundles and C algebras Whose Irreducible Representations are All Finite Dimensional written by Thomas Karl Müller and published by . This book was released on 1990 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Classification and Structure of C Algebra Bundles written by Maurice J. Dupré and published by American Mathematical Soc.. This book was released on 1979 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objects of study in this paper are certain fibre spaces which arise naturally in the representation theory of C*-algebras and locally compact groups. These are a type of Banach bundle, all of whose fibres are C*-algebras. The main aim of this paper is to give a pasting homotopy type classification theory for certain classes of C*-bundles having primarily finite-dimensional fibres and thus classifying the resulting second-order bundles.
Download or read book Mathematical Foundations of Quantum Theory written by A.R. Marlow and published by Elsevier. This book was released on 2012-12-02 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.
Download or read book Dissertationes Mathematicae written by and published by . This book was released on 1995 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book C Algebras by Example written by Kenneth R. Davidson and published by American Mathematical Society, Fields Institute. This book was released on 2023-10-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of $K$-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty years has been based on a careful study of these special classes. While there are many books on C*-algebras and operator algebras available, this is the first one to attempt to explain the real examples that researchers use to test their hypotheses. Topics include AF algebras, Bunce–Deddens and Cuntz algebras, the Toeplitz algebra, irrational rotation algebras, group C*-algebras, discrete crossed products, abelian C*-algebras (spectral theory and approximate unitary equivalence) and extensions. It also introduces many modern concepts and results in the subject such as real rank zero algebras, topological stable rank, quasidiagonality, and various new constructions. These notes were compiled during the author's participation in the special year on C*-algebras at The Fields Institute for Research in Mathematical Sciences during the 1994–1995 academic year. The field of C*-algebras touches upon many other areas of mathematics such as group representations, dynamical systems, physics, $K$-theory, and topology. The variety of examples offered in this text expose the student to many of these connections. Graduate students with a solid course in functional analysis should be able to read this book. This should prepare them to read much of the current literature. This book is reasonably self-contained, and the author has provided results from other areas when necessary.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2006 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book C algebras written by Jacques Dixmier and published by . This book was released on 1982 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost four-fifths of this book deals with the study of C*-algebras, and the main results due, among others, to Fell, Glimm, Kadison, Kaplansky, Mackey and Segal are expounded. Because of the amount of material accumulated on unitary representations of groups, the latter pages of the book are devoted to a brief account of some aspects of this subject, particularly since the theory of groups provides some of the most interesting examples of C*-algebras. The theory of C*-algebras is still expanding rapidly, but this work remains a clear and accessible introduction to the fundamentals of the subject.
Download or read book Rozprawy Matematyczne written by and published by . This book was released on 1991 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Semi simplicial Approach to Foliations and Their Transverse Structure written by Grzegorz Andrzejczak and published by . This book was released on 1991 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Primitivity and the Unital Full Free Product of Finite Dimensional C algebras written by Francisco Torres Ayala and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A C*-algebra is called primitive if it admits a *-representation that is both faithful and irreducible. Thus the simplest examples are matrix algebras. The main objective of this work is to classify unital full free products of finite dimensional C*-algebras that are primitive. We prove that given two nontrivial finite dimensional C*-algebras, A1 /= C, A2 /= C, the unital C*-algebra full free product A = A1 * A2 is primitive except when A1 = C^2 = A2. Roughly speaking, we first show that, except for trivial cases and the case A1 = C^2 = A2, there is an abundance of irreducible finite dimensional *-representations of A. The latter is accomplished by taking advantage of the structure of Lie group of the unitary operators in a finite dimensional Hilbert space. Later, by means of a sequence of approximations and Kaplansky's density theorem we construct an irreducible and faithful {representation of A. We want to emphasize the fact that unital full free products of C*-algebras are highly abstract objects hence finding an irreducible *-{representation that is faithfully is an amazing fact. The dissertation is divided as follows. Chapter I gives an introduction, basic definitions and examples. Chapter II recalls some facts about *-automorphisms of finite dimensional C -algebras. Chapter III is fully devoted to prove Theorem III. 6 which is about perturbing a pair of proper unital C*-subalgebras of a matrix algebra in such a way that they have trivial intersection. Theorem III. 6 is the cornerstone for the rest of the results in this work. Lastly, Chapter IV contains the proof of the main theorem about primitivity and some consequences.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classification of Inductive Limits of Continuous Trace C Algebras written by Cristian Ivanescu and published by LAP Lambert Academic Publishing. This book was released on 2009-06-17 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely, the class of simple C*-algebras which are inductive limits of continuous trace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0,1]. In particular, a classification of simple stably AI algebras is obtained. Also, the range of the invariant is calculated. We start by approximating the building blocks appearing in a given inductive limit decomposition by certain special building blocks. The special building blocks are continuous trace C*-algebras with finite dimensional irreducible representations and such that the dimension of the representations, as a function on the interval, is a finite (lower semicontinuous) step function. It is then proved that these C*-algebras have finite presentations and stable relations. The advantage of having inductive limits of special subhomogeneous algebras is that we can prove the existence of certain gaps for the induced maps between the affine function spaces. These gaps are necessary to prove the Existence Theorem. Also the Uniqueness theorem is proved for these special building blocks.
Download or read book An Introduction to C Algebras and Noncommutative Geometry written by Heath Emerson and published by Springer Nature. This book was released on with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Variables on Boolean and Heyting Algebras and Their Numerical Characteristics written by Ewa Rydzyńska and published by . This book was released on 1990 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Hahn Banach Theorem Surveyed written by Gerard Buskes and published by . This book was released on 1993 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1989 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classification of Ring and C algebra Direct Limits of Finite dimensional Semisimple Real Algebras written by K. R. Goodearl and published by . This book was released on 1987 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:
