Expected publication date is October 18, 2002
Description
This is one of the few books available in the literature that contains problems devoted entirely to the theory of operators on Banach spaces and Banach lattices. The book contains complete solutions to the more than 600 exercises in the companion volume, An Invitation to Operator Theory Volume 50 in the AMS series Graduate Studies in Mathematics, also by Abramovich and Aliprantis.
The exercises and solutions contained in this volume serve many purposes. First, they provide an opportunity to the readers to test their understanding of the theory. Second, they are used to demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Third, the exercises include many well-known results whose proofs are not readily available elsewhere. Finally, the book contains a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible.
The book can be very useful as a supplementary text to graduate courses in operator theory, real analysis, function theory, integration theory, measure theory, and functional analysis. It will also make a nice reference tool for researchers in physics, engineering, economics, and finance.
Contents
・Odds and ends ・Basic operator theory ・Operators on AL- and AM-spaces ・Special classes of operators ・Integral operators ・Spectral properties ・Some special spectra ・Positive matrices ・Irreducible operators ・Invariant subspaces ・The Daugavet equation ・Bibliography ・Index
Details:
Series: Graduate Studies in Mathematics,Volume: 51 Publication Year: 2002 ISBN: 0-8218-2147-4 Paging: 386 pp. Binding: Hardcover
Expected publication date is October 31, 2002
Description
This research monograph presents many new results in a rapidly developing area of great current interest. Guillemin, Ginzburg, and Karshon show that the underlying topological thread in the computation of invariants of G-manifolds is a consequence of a linearization theorem involving equivariant cobordisms. The book incorporates a novel approach and showcases exciting new research.
During the last 20 years, "localization" has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the "quantization commutes with reduction" theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an "abstract moment map". This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics.
The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin{^mathrm{c}}-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Contents
・Introduction ・Part 1. Cobordism Hamiltonian cobordism Abstract moment maps The linearization theorem Reduction and applications ・Part 2. Quantization Geometric quantization The quantum version of the linearization theorem Quantization commutes with reduction ・Part 3. Appendices Signs and normalization conventions Proper actions of Lie groups Equivariant cohomology Stable complex and Spin^{mathrm{c}}structures Assignments and abstract moment maps Assignment cohomology Non-degenerate abstract moment maps Characteristic numbers, non-degenerate cobordisms, and non-virtual quantization The Kawasaki Riemann-Roch formula Cobordism invariance of the index of a transversally elliptic operator Bibliography Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 98 Publication Year: 2002 ISBN: 0-8218-0502-9 Paging: 350 pp. Binding: Hardcover
Expected publication date is October 10, 2002
Description This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known researchers report on their work in model theory and set theory with applications to algebra.
The papers of J. Brendle and A. Blass present one of the most interesting areas of set theory. Brendle gives a very detailed and readable account of Shelah's solution for the long-standing problem of mathrm{Con}(mathfrak{d}<mathfrak{a}). It could be used in an advanced graduate seminar on set theory.
Papers by T. Altinel, J. T. Baldwin, R. Grossberg, W. Hodges, T. Hyttinen, O. Lessmann, and B. Zilber deal with questions of model theory from the viewpoint of stability theory. Here, Zilber constructs an omega-stable complete theory of "pseudo-analytic" structures on algebraically closed fields. This result is part of his program of the model-theoretic study of analytic structures by including Hrushovski's method in the analytic context.
The book presents this and further developments in model theory. It is geared toward advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry.
Contents
J. Brendle -- Mad families and iteration theory A. Blass -- Nearly adequate sets J. D. Hamkins -- How tall is the automorphism tower of a group? J. Stavi and J. Vaananen -- Reflection principles for the continuum B. Zilber -- A theory of a generic function with derivations O. Belegradek -- Poly-regular ordered abelian groups V. Tolstykh -- On the logical strength of the automorphism groups of free nilpotent groups T. Altinel -- Classification of the simple groups of finite Morley rank O. Lessmann -- Homogeneous model theory: Existence and categoricity R. Grossberg -- Classification theory for abstract elementary classes J. T. Baldwin -- Forking and multiplicity in first order theories T. Hyttinen -- Groups acting on geometries W. Hodges -- Relative categoricity in linear orderings M. Di Nasso and Y. Zhang -- Nonstandard analysis and an application to the symmetric group on natural numbers M. Di Nasso and M. Forti -- On the ordering of the nonstandard real line A. Bovykin and R. Kaye -- Order-types of models of Peano arithmetic
Details:
Series: Contemporary Mathematics, Volume: 302 Publication Year: 2003 ISBN: 0-8218-2984-X Paging: 285 pp. Binding: Softcover
Expected publication date is November 10, 2002
Description
This volume presents state-of-the-art research in mathematical physics addressed to a broad spectrum of readers, including graduate students, researchers, and others interested in this topic. Contributors to the volume participated in the 13th International Congress on Mathematical Physics held at Imperial College (London, UK). The contributions include, in particular, pedagogical lectures presented at the Young Researchers Symposium (YRS) held in association with the Congress, as well as public lectures given at the Congress, and the contributions from the winners of the Henri Poincare prize.
Contents
A. Ashtekar -- The second black body problem: interface of general relativity, quantum theory and statistical mechanics M. Atiyah -- On the unreasonable effectiveness of physics in mathematics L. J. Biven -- Weak-wave turbulence: a tragic super-hero of turbulence theory A. Connes -- Noncommutative geometry year 2000 A. Ekert -- Quantum computation L. Faddeev -- Advent of the Yang-Mills field G. Jona-Lasinio -- Cross fertilization in theoretical physics: the case of condensed matter and particle physics J. P. Keating -- Random matrices and the Riemann zeta-function V. V. Kisil -- Meeting Descartes and Klein somewhere in a noncommutative space R. Kotecky -- Phase transitions: on a crossroads of probability and analysis S. A. Levin -- Exploring the complex adaptive nature of ecosystems H. A. Posch and W. Thirring -- The classical three-body problem - where is abstract mathematics, physical intuition, computational physics most powerful? D. Ruelle -- Irreversibility revisited G. Hooft -- A confrontation with infinity H.-T. Yau -- Quantum dynamics of many-body systems A. Fokas, J. Halliwell, T. Kibble, and B. Zegarlinski -- Information about lectures by Per Bak and Joel L. Lebowitz
Details:
Publication Year: 2002 ISBN: 0-8218-3223-9 Paging: 271 pp. Binding: Hardcover
Expected publication date is November 21, 2002
Description
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics.
The book will help readers who are not familiar with nonlinear dynamics to understand and enjoy sophisticated modern monographs on dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.
Contents
・Basic concepts ・Zero-dimensional dynamics ・One-dimensional dynamics ・Two-dimensional dynamics ・Systems with 1.5 degrees of freedom ・Systems generated by three-dimensional vector fields ・Lyapunov exponents ・Appendix ・Bibliography ・Index
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 28 Publication Year: 2002 ISBN: 0-8218-3168-2 Paging: approximately 288 pp. Binding: Hardcover