Hilbert C Modules

Author : E. Christopher Lance
Publisher : Cambridge University Press
Page : 144 pages
File Size : 44,8 Mb
Release : 1995-03-16
Category : Mathematics
ISBN : 9780521479103

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Hilbert C*-Modules by E. Christopher Lance Pdf

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clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material.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.

Author : Vladimir Markovich Manuĭlov,Evgeniĭ Vadimovich Troit͡skiĭ
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 43,6 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821889664

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Hilbert C*-modules by Vladimir Markovich Manuĭlov,Evgeniĭ Vadimovich Troit͡skiĭ Pdf

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.

Author : Klaus Thomsen
Publisher : Unknown
Page : 154 pages
File Size : 55,6 Mb
Release : 1988
Category : C*-algebras
ISBN : UOM:39015049296869

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Hilbert C*-modules, KK-theory and C*-extensions by Klaus Thomsen Pdf

Author : Vladimir Markovich Manuĭlov
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 2005
Category : C*-algebras
ISBN : 1470446502

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Hilbert C*-modules by Vladimir Markovich Manuĭlov Pdf

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.

Author : Vladimir Markovich Manuĭlov,Evgeniĭ Vadimovich Troit͡skiĭ
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 55,7 Mb
Release : 2005
Category : Mathematics
ISBN : 0821838105

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Hilbert C*-modules by Vladimir Markovich Manuĭlov,Evgeniĭ Vadimovich Troit͡skiĭ Pdf

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.

Author : Lunchuan Zhang
Publisher : Springer Nature
Page : 222 pages
File Size : 41,8 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789819986682

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Hilbert C*- Modules and Quantum Markov Semigroups by Lunchuan Zhang Pdf

Author : R. N. Mohapatra,S. Yugesh,G. Kalpana,C. Kalaivani
Publisher : Springer Nature
Page : 661 pages
File Size : 45,5 Mb
Release : 2021-05-05
Category : Mathematics
ISBN : 9789813346468

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Mathematical Analysis and Computing by R. N. Mohapatra,S. Yugesh,G. Kalpana,C. Kalaivani Pdf

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.

Author : Konrad Schmüdgen
Publisher : Springer Nature
Page : 381 pages
File Size : 46,5 Mb
Release : 2020-07-28
Category : Mathematics
ISBN : 9783030463663

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An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space by Konrad Schmüdgen Pdf

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.

Author : Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Publisher : Springer
Page : 425 pages
File Size : 55,5 Mb
Release : 2019-03-11
Category : Mathematics
ISBN : 9783030011567

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Geometric Methods in Physics XXXVI by Piotr Kielanowski,Anatol Odzijewicz,Emma Previato Pdf

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.

Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 50,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803462

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Hilbert Modules over Operator Algebras by Paul S. Muhly,Baruch Solel Pdf

This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.

Author : Ronald G. Douglas,Vern I. Paulsen
Publisher : Longman
Page : 150 pages
File Size : 43,9 Mb
Release : 1989
Category : Function algebras
ISBN : UCAL:B4405659

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Hilbert Modules Over Function Algebras by Ronald G. Douglas,Vern I. Paulsen Pdf

Author : Peter A. Fillmore,James A. Mingo
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 47,6 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821871218

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Operator Algebras and Their Applications by Peter A. Fillmore,James A. Mingo Pdf

The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?

Author : Iain Raeburn,Dana P. Williams
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 44,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808603

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Morita Equivalence and Continuous-Trace $C^*$-Algebras by Iain Raeburn,Dana P. Williams Pdf

A modern treatment of this complex mathematical topic for students beginning research in operator algebras as well as mathematical physicists. Topics include the algebra of compact operators, sheaves, cohomology, the Brauer group and group actions, and the imprimivity theorem. The authors assume a knowledge of C*-algebras, the Gelfand-Naimark Theorem, continuous functional calculus, positivity, and the GNS- construction. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Dan Popovici
Publisher : Unknown
Page : 24 pages
File Size : 43,7 Mb
Release : 1996
Category : C*-algebras
ISBN : UVA:X004169666

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Minimal Unitary Dilations of Contractions on Hilbert C*-modules by Dan Popovici Pdf

Author : Jean Renault
Publisher : Springer
Page : 164 pages
File Size : 52,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540392187

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A Groupoid Approach to C*-Algebras by Jean Renault Pdf