C*-Algebras by Example - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook C*-Algebras by Example write by Kenneth R. Davidson. This book was released on 2023-10-04. C*-Algebras by Example available in PDF, EPUB and Kindle. 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.
C*-Algebras and Operator Theory
C*-Algebras and Operator Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook C*-Algebras and Operator Theory write by Gerald J. Murphy. This book was released on 2014-06-28. C*-Algebras and Operator Theory available in PDF, EPUB and Kindle. This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.
An Introduction to C*-Algebras and the Classification Program
An Introduction to C*-Algebras and the Classification Program - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to C*-Algebras and the Classification Program write by Karen R. Strung. This book was released on 2020-12-15. An Introduction to C*-Algebras and the Classification Program available in PDF, EPUB and Kindle. This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
An Invitation to C*-Algebras
An Invitation to C*-Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to C*-Algebras write by W. Arveson. This book was released on 1998-03-23. An Invitation to C*-Algebras available in PDF, EPUB and Kindle. This book gives an introduction to C*-algebras and their representations on Hilbert spaces. We have tried to present only what we believe are the most basic ideas, as simply and concretely as we could. So whenever it is convenient (and it usually is), Hilbert spaces become separable and C*-algebras become GCR. This practice probably creates an impression that nothing of value is known about other C*-algebras. Of course that is not true. But insofar as representations are con cerned, we can point to the empirical fact that to this day no one has given a concrete parametric description of even the irreducible representations of any C*-algebra which is not GCR. Indeed, there is metamathematical evidence which strongly suggests that no one ever will (see the discussion at the end of Section 3. 4). Occasionally, when the idea behind the proof of a general theorem is exposed very clearly in a special case, we prove only the special case and relegate generalizations to the exercises. In effect, we have systematically eschewed the Bourbaki tradition. We have also tried to take into account the interests of a variety of readers. For example, the multiplicity theory for normal operators is contained in Sections 2. 1 and 2. 2. (it would be desirable but not necessary to include Section 1. 1 as well), whereas someone interested in Borel structures could read Chapter 3 separately. Chapter I could be used as a bare-bones introduction to C*-algebras. Sections 2.
C*-Algebras and W*-Algebras
C*-Algebras and W*-Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook C*-Algebras and W*-Algebras write by Shoichiro Sakai. This book was released on 2012-12-06. C*-Algebras and W*-Algebras available in PDF, EPUB and Kindle. From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews
