Hilbert C*-Modules

Hilbert C*-Modules PDF

Author: E. Christopher Lance

Publisher: Cambridge University Press

Published: 1995-03-16

Total Pages: 144

ISBN-13: 052147910X

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Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.

Hilbert C*-modules

Hilbert C*-modules PDF

Author: Vladimir Markovich Manuĭlov

Publisher: American Mathematical Soc.

Published:

Total Pages: 216

ISBN-13: 9780821889664

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Based on lectures delivered by the authors at Moscow State University, this volume presents a detailed introduction to the theory of Hilbert $C*$-modules. Hilbert $C*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C $ is replaced by an arbitrary $C*$-algebra. The general theory of Hilbert $C*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool inoperator algebras theory, index theory of elliptic operators, $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C*$-modules is interesting on its own. In this book, the authors explain in detail the basic notions and results of thetheory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

Hilbert C*-modules

Hilbert C*-modules PDF

Author: Vladimir Markovich Manuĭlov

Publisher:

Published: 2005

Total Pages:

ISBN-13: 9781470446505

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Hilbert C^*-modules provide a natural generalization of Hilbert spaces arising when the field of scalars \mathbf{C} is replaced by an arbitrary C^*-algebra. The general theory of Hilbert C^*-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, in index theory of elliptic operators, in K- and KK-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert C^*-modules is interesting on its own. The present book is an introduction to the theory of Hi.

Hilbert C*-modules

Hilbert C*-modules PDF

Author: Vladimir Markovich Manuĭlov

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 202

ISBN-13: 9780821838105

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Hilbert $C^*$-modules provide a natural generalization of Hilbert spaces arising when the field of scalars $\mathbf{C}$ is replaced by an arbitrary $C^*$-algebra. The general theory of Hilbert $C^*$-modules appeared more than 30 years ago in the pioneering papers of W. Paschke and M. Rieffel and has proved to be a powerful tool in operator algebras theory, in index theory of elliptic operators, in $K$- and $KK$-theory, and in noncommutative geometry as a whole. Alongside these applications, the theory of Hilbert $C^*$-modules is interesting on its own. The present book is an introduction to the theory of Hilbert $C^*$-modules. The authors explain in detail the basic notions and results of the theory, and provide a number of important examples. Some results related to the authors' research interests are also included. A large part of the book is devoted to structural results (self-duality, reflexivity) and to nonadjointable operators. Most of the book can be read with only a basic knowledge of functional analysis; however, some experience in the theory of operator algebras makes reading easier.

Geometric Methods in Physics XXXVI

Geometric Methods in Physics XXXVI PDF

Author: Piotr Kielanowski

Publisher: Springer

Published: 2019-03-11

Total Pages: 425

ISBN-13: 3030011569

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This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Mathematical Analysis and Computing

Mathematical Analysis and Computing PDF

Author: R. N. Mohapatra

Publisher: Springer Nature

Published: 2021-05-05

Total Pages: 661

ISBN-13: 9813346469

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This book is a collection of selected papers presented at the International Conference on Mathematical Analysis and Computing (ICMAC 2019) held at Sri Sivasubramaniya Nadar College of Engineering, Chennai, India, from 23–24 December 2019. Having found its applications in game theory, economics, and operations research, mathematical analysis plays an important role in analyzing models of physical systems and provides a sound logical base for problems stated in a qualitative manner. This book aims at disseminating recent advances in areas of mathematical analysis, soft computing, approximation and optimization through original research articles and expository survey papers. This book will be of value to research scholars, professors, and industrialists working in these areas.

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space PDF

Author: Konrad Schmüdgen

Publisher: Springer Nature

Published: 2020-07-28

Total Pages: 381

ISBN-13: 3030463664

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This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

Hilbert Modules over Operator Algebras

Hilbert Modules over Operator Algebras PDF

Author: Paul S. Muhly

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 69

ISBN-13: 0821803468

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Addresses the three-dimensional generalization of category, offering a full definition of tricategory; a proof of the coherence theorem for tricategories; and a modern source of material on Gray's tensor product of 2-categories. Of interest to research mathematicians; theoretical physicists, algebraic topologists; 3-D computer scientists; and theoretical computer scientists. Society members, $19.00. No index. Annotation copyright by Book News, Inc., Portland, OR

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