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Topological and Bivariant K-theory
Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras.
Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces
Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is put on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details.
Recent Advances in Operator Theory, Operator Algebras, and their Applications ; XIXth International Conference on Operator Theory, Timisoara (Romania), 2002
The Romanian conferences in operator theory, as they are now commonly called, have started in the year1976 as an annual workshop on operator theory held at the University of Timi¸ soara, originally only with Romanian attendance. The meeting soon evolved into an international conference, with an increasingly larger parti- pation. It has been organized jointly, initially by the Department of Mathematics of INCREST and by the Faculty of Sciences of the University of Timi¸ soara, then (since 1990) by the Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timi¸ soara.
Operator Algebras, Toeplitz Operators and Related Topics
Features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications.
Operator Algebras, Operator Theory and Applications
Composed of three survey lecture courses and nineteen invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory.
Operator Algebras ; Vol.122 : Theory of C*-Algebras and von Neumann Algebras
Attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of the subject, how does this volume make asignificant addition to the literature, and how does it difier from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the first paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume.
Operator Algebras ; Vol.1 : The Abel Symposium 2004
Part of a book series linked to the Abel prize, this book the theme of the first Abel Symposium - operator algebras. Operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry.
Open Quantum Systems III : Recent Developments
Present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.
Open Quantum Systems II : The Markovian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications.
Open Quantum Systems I : The Hamiltonian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. This Volume, I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.
Infinite groups : geometric, combinatorial and dynamical aspects
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others.
Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Dynamical Entropy in Operator Algebras
The book including quantum dynamical systems and applications of operator algebras and ergodic theory. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
