An Invitation To Unbounded Representations Of Algebras On Hilbert Space

Author : Konrad Schmüdgen
Publisher : Springer Nature
ISBN 13 : 3030463664
Total Pages : 381 pages
Book Rating : 4.63/5 ( download)

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Download or read book An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space written by Konrad Schmüdgen and published by Springer Nature. This book was released on 2020-07-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maria Fragoulopoulou
Publisher : Springer Nature
ISBN 13 : 3030964337
Total Pages : 251 pages
Book Rating : 4.37/5 ( download)

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Download or read book Generalized B*-Algebras and Applications written by Maria Fragoulopoulou and published by Springer Nature. This book was released on 2022-06-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Atsushi Inoue
Publisher :
ISBN 13 : 9783030688943
Total Pages : 0 pages
Book Rating : 4.41/5 ( download)

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Download or read book Tomita's Lectures on Observable Algebras in Hilbert Space written by Atsushi Inoue and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. .

Author :
Publisher : Elsevier
ISBN 13 : 008052835X
Total Pages : 597 pages
Book Rating : 4.59/5 ( download)

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Download or read book Hilbert Spaces written by and published by Elsevier. This book was released on 2001-07-11 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition – Theorem – Proof - Example - Exercises . The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.

Author : Robert Barr Smith
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.44/5 ( download)

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Download or read book Representation of Certain Algebras on Hilbert Space written by Robert Barr Smith and published by . This book was released on 1957 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bertram Kostant
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.48/5 ( download)

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Download or read book Representations of a Lie Algebra and Its Enveloping Algebra on Hilbert Space written by Bertram Kostant and published by . This book was released on 1954 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J. M.G. Fell
Publisher : Academic Press
ISBN 13 : 0080874452
Total Pages : 755 pages
Book Rating : 4.56/5 ( download)

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Download or read book Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles written by J. M.G. Fell and published by Academic Press. This book was released on 1988-05-01 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Author : J. M.G. Fell
Publisher : Academic Press
ISBN 13 : 0080874444
Total Pages : 771 pages
Book Rating : 4.49/5 ( download)

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Download or read book Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles written by J. M.G. Fell and published by Academic Press. This book was released on 1988-04-15 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Author : Elmar Wagner
Publisher :
ISBN 13 :
Total Pages : 103 pages
Book Rating : 4.27/5 ( download)

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Download or read book Hilbert Space Representations of Some Quantum Algebras written by Elmar Wagner and published by . This book was released on 2002 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M. Takesaki
Publisher : Springer
ISBN 13 : 3540362673
Total Pages : 126 pages
Book Rating : 4.78/5 ( download)

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Download or read book Tomita's Theory of Modular Hilbert Algebras and its Applications written by M. Takesaki and published by Springer. This book was released on 2006-11-15 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: