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Operator Algebras And Applications

Author: David E. Evans
Publisher: Cambridge University Press
ISBN: 0521368448
Size: 32.72 MB
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These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

The Technique Of Pseudodifferential Operators

Author: H. O. Cordes
Publisher: Cambridge University Press
ISBN: 9780521378642
Size: 32.65 MB
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Pseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.

Double Affine Hecke Algebras

Author: Ivan Cherednik
Publisher: Cambridge University Press
ISBN: 0521609186
Size: 30.19 MB
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This is an essentially self-contained monograph centered on the new double Hecke algebra technique.

An Introduction To K Theory For C Algebras

Author: M. Rørdam
Publisher: Cambridge University Press
ISBN: 9780521789448
Size: 80.87 MB
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This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

C Algebras And Finite Dimensional Approximations

Author: Nathanial Patrick Brown
Publisher: American Mathematical Soc.
ISBN: 0821843818
Size: 43.74 MB
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$\mathrm{C}^*$-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 $\mathrm{C}^*$-approximation theory.

Operator Algebras And Their Applications

Author: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 1470419483
Size: 35.21 MB
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his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.