An Invitation To Unbounded Representations Of Algebras On Hilbert Space

Author : Konrad Schmüdgen
Publisher : Springer Nature
Page : 381 pages
File Size : 54,6 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 : K. Schmüdgen
Publisher : Walter de Gruyter GmbH & Co KG
Page : 380 pages
File Size : 54,9 Mb
Release : 1990-12-31
Category : Mathematics
ISBN : 9783112715734

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Unbounded Operator Algebras and Representation Theory by K. Schmüdgen Pdf

No detailed description available for "Unbounded Operator Algebras and Representation Theory".

Author : Konrad Schmüdgen
Publisher : Birkhauser
Page : 388 pages
File Size : 51,8 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018970353

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Unbounded Operator Algebras and Representation Theory by Konrad Schmüdgen Pdf

Author : William Arveson
Publisher : Unknown
Page : 124 pages
File Size : 45,6 Mb
Release : 1976
Category : Electronic
ISBN : 1461263727

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An invitation to C-algebras by William Arveson Pdf

Author : Maria Fragoulopoulou,Atsushi Inoue,Martin Weigt,Ioannis Zarakas
Publisher : Springer Nature
Page : 251 pages
File Size : 46,7 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9783030964337

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Generalized B*-Algebras and Applications by Maria Fragoulopoulou,Atsushi Inoue,Martin Weigt,Ioannis Zarakas Pdf

This book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand–Naimark type theorems, a Vidav–Palmer type theorem, an unbounded representation theory, and miscellaneous applications. Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.

Author : William Arveson
Publisher : Unknown
Page : 106 pages
File Size : 47,7 Mb
Release : 1976-01
Category : C*-algebras
ISBN : 3540901760

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An Invitation to C*-algebras by William Arveson Pdf

Author : J-P Antoine,I. Inoue,C. Trapani
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 44,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401700658

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Partial *- Algebras and Their Operator Realizations by J-P Antoine,I. Inoue,C. Trapani Pdf

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).

Author : Jorgensen Palle,Tian Feng
Publisher : World Scientific
Page : 564 pages
File Size : 54,5 Mb
Release : 2017-01-24
Category : Mathematics
ISBN : 9789813202146

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Non-commutative Analysis by Jorgensen Palle,Tian Feng Pdf

The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret "non-commutative analysis" broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.) A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras. The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

Author : William Arveson
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 43,8 Mb
Release : 1984
Category : Mathematics
ISBN : 0821889001

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Ten Lectures on Operator Algebras by William Arveson Pdf

This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.

Author : Tsoy–Wo Ma
Publisher : World Scientific Publishing Company
Page : 620 pages
File Size : 51,6 Mb
Release : 2002-06-13
Category : Mathematics
ISBN : 9789813105980

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Banach–Hilbert Spaces, Vector Measures and Group Representations by Tsoy–Wo Ma Pdf

This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations. It contains a full treatment of vector measures on delta rings without assuming any scalar measure theory and hence should fit well into existing courses. The relation between group representations and almost periodic functions is presented. The mean values offer an infinitedimensional analogue of measure theory on finitedimensional Euclidean spaces. This book is ideal for beginners who want to get through the basic material as soon as possible and then do their own research immediately.

Author : Charles W. Groetsch
Publisher : Springer
Page : 133 pages
File Size : 41,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540399438

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Stable Approximate Evaluation of Unbounded Operators by Charles W. Groetsch Pdf

This book teams up the spectral theory of bounded linear operators with von Neumann’s theory of unbounded operators to provide a framework for the study of stable methods for the evaluation of unbounded operators. The text presents numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. It also offers an extensive exposition of background material from the theory of operators on Hilbert space.

Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 72 pages
File Size : 45,9 Mb
Release : 1995-09-28
Category : Mathematics
ISBN : 0821862820

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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 : ChunLan Jiang
Publisher : Taylor & Francis
Page : 256 pages
File Size : 51,8 Mb
Release : 2023-02-15
Category : Mathematics
ISBN : 9781351413305

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Strongly Irreducible Operators on Hilbert Space by ChunLan Jiang Pdf

This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.

Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 48,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872840

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Infinite-dimensional Representations of 2-groups by John C. Baez Pdf

A “$2$-group'' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on “$2$-vector spaces'', which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called ``measurable categories'' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.

They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$-intertwiners for any skeletal measurable $2$-group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study “irretractable'' representations--another feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered “separable $2$-Hilbert spaces'', and compare this idea to a tentative definition of $2$-Hilbert spaces as representation categories of commutative von Neumann algebras.

Author : Maria Fragoulopoulou,Camillo Trapani
Publisher : Springer
Page : 262 pages
File Size : 49,8 Mb
Release : 2020-04-08
Category : Mathematics
ISBN : 3030377040

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Locally Convex Quasi *-Algebras and their Representations by Maria Fragoulopoulou,Camillo Trapani Pdf

This book offers a review of the theory of locally convex quasi *-algebras, authored by two of its contributors over the last 25 years. Quasi *-algebras are partial algebraic structures that are motivated by certain applications in Mathematical Physics. They arise in a natural way by completing a *-algebra under a locally convex *-algebra topology, with respect to which the multiplication is separately continuous. Among other things, the book presents an unbounded representation theory of quasi *-algebras, together with an analysis of normed quasi *-algebras, their spectral theory and a study of the structure of locally convex quasi *-algebras. Special attention is given to the case where the locally convex quasi *-algebra is obtained by completing a C*-algebra under a locally convex *-algebra topology, coarser than the C*-topology. Introducing the subject to graduate students and researchers wishing to build on their knowledge of the usual theory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.