C*-Algebras and Finite-Dimensional Approximations (Graduate Studies in Mathematics) by Nathanial P. Brown and Narutaka Ozawa (PDF)

Description

$textrm{C}^*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications–written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $textrm{C}^*$-approximation theory.

User’s Reviews

Editorial Reviews: Review “This exciting book takes its readers through a wide palette of topics of current interest within operator algebras and operator space theory. … These authors have succeeded very well in writing a book that is at the same time a textbook for (graduate) students and a research monograph for experts. …the entire book makes for enjoyable reading for both types of readers thanks to its clear, informal and witty style. Each section ends with a list of appetizing exercises. …no other book so far has taken this particular charming path through the landscapes of operator algebras.” —- Mathematical Reviews

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