Partial *- Algebras and Their Operator Realizations

Author: Jean-Pierre ANTOINE,Atsushi Inoue,C. Trapani

Publisher: Springer Science & Business Media

ISBN: 9401700656

Category: Mathematics

Page: 522

View: 6313

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).
Posted in Mathematics

Topological Algebras and Applications

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

Page: 442

View: 7843

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.
Posted in Mathematics

Proceedings of the Third International Workshop on Contemporary Problems in Mathematical Physics

Cotonou, Republic of Benin, 1-7 November 2003

Author: Jan Govaerts

Publisher: World Scientific

ISBN: 9789812702487

Category: Electronic books

Page: 628

View: 3680

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: OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings)OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)OCo CC Proceedings OCo Engineering & Physical Sciences"
Posted in Electronic books

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7216

Posted in Mathematics

A Panorama of Modern Operator Theory and Related Topics

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

Page: 642

View: 6292

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.
Posted in Mathematics

Topological Algebras, Their Applications, and Related Topics

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

ISBN: N.A

Category: Topological algebras

Page: 411

View: 780

Posted in Topological algebras

Current Trends In Operator Theory And Its Applications

Author: Joseph A. Ball

Publisher: Springer Science & Business Media

ISBN: 9783764370671

Category: Language Arts & Disciplines

Page: 595

View: 463

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.
Posted in Language Arts & Disciplines

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

With Applications to Rigorous Quantum Field Theory

Author: József Lörinczi,Fumio Hiroshima,Volker Betz

Publisher: Walter de Gruyter

ISBN: 3110203731

Category: Mathematics

Page: 516

View: 1594

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.
Posted in Mathematics

Contributions in mathematical physics

a tribute to Gerard G. Emch

Author: Gérard G. Emch,Syed Twareque Ali

Publisher: N.A

ISBN: 9788185931791

Category: Mathematical physics

Page: 217

View: 5209

Gérard G. Emch, b. 1936, mathematical physicist and quantum mechanic; contributed articles.
Posted in Mathematical physics

Note Di Matematica

Author: R. Marinosci

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7082

Posted in Mathematics

Vertex Operators in Mathematics and Physics

Proceedings of a Conference November 10–17, 1983

Author: J. Lepowsky,S. Mandelstam,I.M. Singer

Publisher: Springer Science & Business Media

ISBN: 146139550X

Category: Science

Page: 482

View: 9189

James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Posted in Science

Lie Theory and Its Applications in Physics

IX International Workshop

Author: Vladimir Dobrev

Publisher: Springer Science & Business Media

ISBN: 4431542701

Category: Mathematics

Page: 554

View: 7688

Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics” held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.
Posted in Mathematics

Unbounded Operator Algebras and Representation Theory

Author: K. Schmüdgen

Publisher: Birkhäuser

ISBN: 3034874693

Category: Mathematics

Page: 368

View: 9576

*-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Posted in Mathematics

Reviews in operator theory, 1980-86

as printed in Mathematical reviews

Author: American mathematical society

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 2328

View: 9214

Posted in Mathematics

Issues in General and Specialized Mathematics Research: 2011 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1464964920

Category: Mathematics

Page: 862

View: 9918

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/.
Posted in Mathematics