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Tomita Takesaki Theory In Algebras Of Unbounded Operators

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Tomita Takesaki Theory In Algebras Of Unbounded Operators

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Author : Atsushi Inoue
language : en
Publisher: Springer
Release Date : 2006-11-14

Tomita Takesaki Theory In Algebras Of Unbounded Operators written by Atsushi Inoue and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.

Tomita Takesaki Theory In Algebras Of Unbounded Operators

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Author : Atsushi Inoue
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1998-11-18

Tomita Takesaki Theory In Algebras Of Unbounded Operators written by Atsushi Inoue and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-18 with Computers categories.

Topological Algebras And Applications

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Author : Anastasios Mallios
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Topological Algebras And Applications written by Anastasios Mallios and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Tomita S Lectures On Observable Algebras In Hilbert Space

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Author : Atsushi Inoue
language : en
Publisher: Springer Nature
Release Date : 2021-03-01

Tomita S Lectures On Observable Algebras In Hilbert Space written by Atsushi Inoue and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-01 with Mathematics categories.

This book is devoted to the study of Tomita's observable algebras, their structure and applications. It begins by building the foundations of the theory of T*-algebras and CT*-algebras, presenting the major results and investigating the relationship between the operator and vector representations of a CT*-algebra. It is then shown via the representation theory of locally convex*-algebras that this theory includes Tomita–Takesaki theory as a special case; every observable algebra can be regarded as an operator algebra on a Pontryagin space with codimension 1. All of the results are proved in detail and the basic theory of operator algebras on Hilbert space is summarized in an appendix. The theory of CT*-algebras has connections with many other branches of functional analysis and with quantum mechanics. The aim of this book is to make Tomita’s theory available to a wider audience, with the hope that it will be used by operator algebraists and researchers in these related fields.

Partial Algebras And Their Operator Realizations

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Author : J-P Antoine
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Partial Algebras And Their Operator Realizations written by J-P Antoine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

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 With Involution

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Author : M. Fragoulopoulou
language : en
Publisher: Elsevier
Release Date : 2005-07-26

Topological Algebras With Involution written by M. Fragoulopoulou and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-26 with Mathematics categories.

This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.Key features:- Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers.- Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.

Topology Of Singular Fibers Of Differentiable Maps

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Author : Osamu Saeki
language : en
Publisher: Springer Science & Business Media
Release Date : 2004

Topology Of Singular Fibers Of Differentiable Maps written by Osamu Saeki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Differentiable mappings categories.

Finite Or Infinite Dimensional Complex Analysis And Applications

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Author : Le Hung Son
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Finite Or Infinite Dimensional Complex Analysis And Applications written by Le Hung Son and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took place in Hanoi from August 8 - 12, 2001. This conference th was the 9 one in a series of conferences which take place alternately in China, Japan, Korea and Vietnam each year. The first one took place th at Pusan University in Korea in 1993. The preceding 8 conference was th held in Shandong in China in August 2000. The 9 conference of the was the first one which took place above mentioned series of conferences in Vietnam. Present trends in Complex Analysis reflected in the present volume are mainly concentrated in the following four research directions: 1 Value distribution theory (including meromorphic funtions, mero morphic mappings, as well as p-adic functions over fields of finite or zero characteristic) and its applications, 2 Holomorphic functions in several (finitely or infinitely many) com plex variables, 3 Clifford Analysis, i.e., complex methods in higher-dimensional real Euclidian spaces, 4 Generalized analytic functions.

Seminaire De Probabilites Xxxiii

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Author : J. Azema
language : en
Publisher: Springer
Release Date : 2006-11-14

Seminaire De Probabilites Xxxiii written by J. Azema and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Besides topics traditionally found in the Sminaire de Probabilits (Martingale Theory, Stochastic Processes, questions of general interest in Probability Theory), this volume XXXIII presents nine contributions to the study of filtrations up to isomorphism. It also contains three graduate courses: Dynamics of stochastic algorithms, by M. Benaim; Simulated annealing algorithms and Markov chains with rare transitions, by O. Catoni; and Concentration of measure and logarithmic Sobolev inequalities, by M. Ledoux. These up to date courses present the state of the art in three matters of interest to students in theoretical or applied Probability Theory, and to researchers as well.

Periodic Solutions Of The N Body Problem

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Author : Kenneth R. Meyer
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-11-17

Periodic Solutions Of The N Body Problem written by Kenneth R. Meyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-17 with Mathematics categories.

Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.

Tomita Takesaki Theory In Algebras Of Unbounded Operators

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