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The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C•-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C•-algebras and symbolic dynamics. more...

This book features papers presented during a special session on algebra, functional analysis, complex analysis, and pluripotential theory. Research articles focus on topics such as slow convergence, spectral expansion, holomorphic extension, m-subharmonic functions, pseudo-Galilean group, involutive algebra, Log-integrable measurable functions, Gibbs measures, harmonic and analytic functions, local automorphisms, Lie algebras, and Leibniz algebras. Many of the papers address the theory of harmonic functions, and the book includes a number of extensive survey papers. Graduate and researchers interested in functional analysis, complex analysis, operator algebras and non-associative algebras will find this book relevant to their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference's scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Differential Equations and Dynamical Systems is also published in the Springer Proceedings in Mathematics & Statistics Series. more...

The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20–23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan. This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrödinger operators, convexity and dynamical systems. more...

This book contains a collection of articles provided by the participants of the SFB-workshop on C•-algebras, March 8 - March 12, 1999 which was held at the Sonderforschungsbereich'Geometrische Strukturen in der reinen Mathematik'of the University of Münster, Germany. The aim of the workshop was to bring together leading experts in the theory of C• -algebras with promising young researchers in the field, and to provide a stimulating atmosphere for discussions and interactions between the participants. There were 19 one-hour lectures on various topics like - classification of nuclear C• -algebras, - general K-theory for C• -algebras, - exact C• -algebras and exact groups, - C•-algebras associated to (infinite) matrices and C•-correspondences, - noncommutative prob ability theory, - deformation quantization, - group C• -algebras and the Baum-Connes conjecture, giving a broad overview of the latest developments in the field, and serving as a basis for discussions. We, the organizers of the workshop, were greatly pleased with the excellence of the lectures and so were led to the idea of publishing the proceedings of the conference. There are basically two kinds of contributions. On one side there are several articles giving surveys and overviews on new developments and im­ portant results of the theory, on the other side one finds original articles with interesting new results. more...

This volume contains papers presented at the University of Iowa 1985 Summer Conference in honor of H.-J. Borchers, N. M. Hugenholtz, R. V. Kadison, and D. Kastler and gives a systematic, up-to-date treatment of the fruitful interaction that the last two decades have brought between operator algebras and mathematical physics. Special attention is paid to an overview of the algebraic approach to quantum field theory and in particular, to quantum statistical mechanics. More than half the papers culminate with a presentation of new results which have not appeared previously in journals, and with a few exceptions, these new results are presented with complete proofs. This book is addressed to graduate students and researchers working in a broad spectrum of areas in mathematics and mathematical physics. Functional analysis, operator algebras, operator theory, differential geometry, cyclic cohomology, $K$-theory, and index theory are applied to questions in the quantum theory of fields and statistical mechanics. The individual papers are self-contained, but the reader should have some familiarity with the basic concepts of functional analysis and operator theory, although no physics background is assumed. more...

This volume contains the proceedings of an AMS Special Session held at the Joint Mathematics Meetings in San Antonio in January 1993 to celebrate the first fifty years of $C^•$-algebra theory. The book contains carefully written expository and research articles by leaders in the field. Also included is a reprinting of the original 1943 paper on $C^•$-algebras by Gelfand and Neumark, which has had such a profound influence on the field. The volume covers a broad spectrum of topics, including the Gelfand-Neumark theorems, $C^•$-algebras and quantization, projections in $C^•$-algebras, Mackey's theory of group representations and their relation to $C^•$-algebras, transformation group $C^•$-algebras, the influence of algebraic topology on $C^•$-algebras, K-theory and index theory in operator algebras, exponential rank in $C^•$-algebras, and a survey of the development of type III von Neumann algebras. With historical perspectives and up-to-date overviews to orient readers new to the field, this book will interest mathematicians, physicists, and mathematical historians. more...

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers. more...

The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis- pline within functional analysis to become a central?eld in mathematics often described as “non-commutative geometry” (see for example the book “Non-Commutative Geometry” by the Fields medalist Alain Connes). It has branched out in several sub-disciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn- ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the?eld were willing to contribute. The basic?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite - mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral - erators. An important feature is that the composition of two operators is a non-commutative operation. more...

This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of $C^•$-algebras and von Neumann algebras, together with recent work on the classification of $C^•$-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature. more...