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Search Results for: partial-algebras-and-their-operator-realizations-mathematics-and-its-applications

## Partial *- Algebras and Their Operator Realizations

Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmüdgen [1990] and A. Inoue [1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).
## Topological Algebras and Applications

The Fifth International Conference on Topological Algebras and Applications was held in Athens, Greece, from June 27th to July 1st of 2005. The main topic of the Conference was general theory of topological algebras and its various applications, with emphasis on the ""non-normed"" case. In addition to the study of the internal structure of non-normed, and even non-locally convex topological algebras, there are applications to other branches of mathematics, such as differential geometry of smooth manifolds, and mathematical physics, such as quantum relativity and quantum cosmology. Operator theory of unbounded operators and related non-normed topological algebras are intensively studied here. Other topics presented in this volume are topological homological algebra, topological algebraic geometry, sheaf theory and $K$-theory.
## Contemporary Problems in Mathematical Physics

The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their physics applications can be conceived, developed and disseminated. Basic ideas for addressing a variety of contemporary problems in mathematical and theoretical physics are presented in a nonintimidating atmosphere. Experts provide the reader the fundamentals to predict new possibilities in physics and other fields. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Diffeomorphisms Groups in Quantum Physics (G A Goldin)On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field Theory (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:A Stochastic Streamflow Model Based on a Minimum Energy Expenditure Concept (A Afouda et al.)Regge Poles Trajectories for Nonsingular Potentials: The Thomas-Fermi Potentials (Z Felfli et al.)Proposed Differential Equation for Spin 1/2 (H V Mweene)Influence of Diseases and Arterial Prostheses on Solitary Blood Waves: Characteristics of an Ideal Prosthesis (S Noubissié & P Woafo)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Vector Coherent States over Matrix Domains (S T Ali)Wavelet Analysis and Some of Its Applications in Physics (J-P Antoine)Some Variations on the Berezin Quantization Method (M Engliš)Variational Analysis, PDE's and Image Analysis: The Big Picture and a Sampling of Details (N D George & K R Vixie)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Orthogonal Polynomials of Class One (E S Azatassou & M N Hounkonnou)and other papers Readership: Researchers and professionals in physics and mathematics. Keywords:Mathematical Physics;Theoretical Physics;Quantum Physics;Coherent States;Supersymmetry
## Bulletin of the Korean Mathematical Society

## Two-Dimensional Conformal Geometry and Vertex Operator Algebras

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.
## Mathematical Reviews

## A Panorama of Modern Operator Theory and Related Topics

This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.
## Current Trends In Operator Theory And Its Applications

Many developments on the cutting edge of research in operator theory and its applications, and related areas of mathematics, are reflected in this collection of original and review articles. Particular emphasis lies on the applications of operator theory to basic problems in distributed parameter systems, mathematical physics, wavelets, and numerical analysis.Review articles include a report on recent achievements and future directions of research in the area of operator theory and its diverse applications.The intended audience is researchers and graduate students in mathematics, physics, and electrical engineering.
## Journal of the Mathematical Society of Japan

## Topological Algebras, Their Applications, and Related Topics

## Feynman-Kac-Type Theorems and Gibbs Measures on Path Space

This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. These ideas are then applied principally to a rigorous treatment of some fundamental models of quantum field theory. In this self-contained presentation of the material both beginners and experts are addressed, while putting emphasis on the interdisciplinary character of the subject.
## Contributions in mathematical physics

Gérard G. Emch, b. 1936, mathematical physicist and quantum mechanic; contributed articles.
## Note Di Matematica

## Realization and Modelling in System Theory

This volume is the first of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathematical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989. The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is typical for MTNS, turns out to be most effective and is, as these proceedings show, a continuing source of exciting advances. The first volume contains invited papers and a large selection of other symposium presentations on the general theory of deterministic and stochastic systems with an emphasis on realization and modelling. A wide variety of recent results on approximate realization and system identification, stochastic dynamical systems, discrete event systems,- o systems, singular systems and nonstandard models IS presented. Preface vi Also a few papers on applications in hydrology and hydraulics are included. The titles of the two other volumes are: Robust Control of Linear Sys tems and Nonlinear Control (volume 2) and Signal Processing. Scatter ing and Operator Theory. and Numerical Methods (volume 3). The Editors are most grateful to the about 300 reviewers for their help in the refereeing process. The Editors thank Ms. G. Bijleveld and Ms.
## American Book Publishing Record

## Abstracts of Papers Presented to the American Mathematical Society

## Featured Reviews in Mathematical Reviews 1997-1999

This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
## The State Space Method

Thisvolumeofthe Operator Theory: Advances and Applications series (OTAA) isthe ?rst volume of a new subseries. This subseries is dedicated to connections between the theory of linear operators and the mathematical theory of linear systems and is named Linear Operators and Linear Systems (LOLS).Asthe- isting subseries Advances in Partial Di?erential Equations (ADPE), the new s- series will continue the traditions of the OTAA series and keep the high quality of the volumes. The editors of the new subseries are: Daniel Alpay (Beer–Sheva, - rael), Joseph Ball (Blacksburg, Virginia, USA) and Andr ́ ́ e Ran (Amsterdam, The Netherlands). In the last 25–30 years, Mathematical System Theory developed in an ess- tial way. A large part of this development was connected with the use of the state space method. Let us mention for instance the “theory of H control”. The state ? space method allowed to introduce in system theory the modern tools of matrix and operator theory. On the other hand the state space approach had an imp- tant impact on Algebra, Analysis and Operator Theory. In particular it allowed to solve explicitly some problems from interpolation theory, theory of convolution equations, inverse problems for canonical di?erential equations and their discrete analogs. All these directions are planned to be present in the subseries LOLS. The editors and the publisher are inviting authors to submit their manuscripts for publication in this subseries.
## Reviews in operator theory, 1980-86

## Issues in General and Specialized Mathematics Research: 2011 Edition

Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

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Author: J-P Antoine,I. Inoue,C. Trapani

Publisher: Springer Science & Business Media

ISBN: 9401700656

Category: Mathematics

Page: 522

View: 5836

*Fifth International Conference on Topological Algebras and Applications, June 27-July 1, 2005, Athens, Greece*

Author: Anastasios Mallios,Marina Haralampidou

Publisher: American Mathematical Soc.

ISBN: 0821838687

Category: Mathematics

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Author: Jan Govaerts,M Norbert Hounkonnou,Alfred Z Msezane

Publisher: World Scientific

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*The Israel Gohberg Memorial Volume*

Author: Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer

Publisher: Springer Science & Business Media

ISBN: 3034802218

Category: Mathematics

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Author: Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman

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*Proceedings of the Conference to Celebrate the 70th Birthday of Wieslaw Zelazko, Bedlewo, May 11-17, 2003*

Author: Krzysztof Jarosz,Andrzej Sołtysiak

Publisher: N.A

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Category: Topological algebras

Page: 411

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*With Applications to Rigorous Quantum Field Theory*

Author: József Lörinczi,Fumio Hiroshima,Volker Betz

Publisher: Walter de Gruyter

ISBN: 3110203731

Category: Mathematics

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*a tribute to Gerard G. Emch*

Author: Gérard G. Emch,Syed Twareque Ali

Publisher: N.A

ISBN: 9788185931791

Category: Mathematical physics

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Author: R. Marinosci

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*Proceedings of the International Symposium MTNS-89*

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ISBN: 146123462X

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*With Selected Reviews of Classic Books and Papers from 1940-1969*

Author: Donald G. Babbitt,Jane E. Kister

Publisher: American Mathematical Soc.

ISBN: 9780821896709

Category: Mathematics

Page: 541

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*Generalizations and Applications*

Author: Daniel Alpay,Israel Gohberg

Publisher: Springer Science & Business Media

ISBN: 3764374314

Category: Mathematics

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*as printed in Mathematical reviews*

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