An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space write by Konrad Schmüdgen. This book was released on 2020-07-28. An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space available in PDF, EPUB and Kindle. 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.
Generalized B*-Algebras and Applications
Generalized B*-Algebras and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized B*-Algebras and Applications write by Maria Fragoulopoulou. This book was released on 2022-06-09. Generalized B*-Algebras and Applications available in PDF, EPUB and Kindle. 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.
Tomita's Lectures on Observable Algebras in Hilbert Space
Tomita's Lectures on Observable Algebras in Hilbert Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tomita's Lectures on Observable Algebras in Hilbert Space write by Atsushi Inoue. This book was released on 2021. Tomita's Lectures on Observable Algebras in Hilbert Space available in PDF, EPUB and Kindle. 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. .
Hilbert Spaces
Hilbert Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert Spaces write by . This book was released on 2001-07-11. Hilbert Spaces available in PDF, EPUB and Kindle. 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.
Representation of Certain Algebras on Hilbert Space
Representation of Certain Algebras on Hilbert Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representation of Certain Algebras on Hilbert Space write by Robert Barr Smith. This book was released on 1957. Representation of Certain Algebras on Hilbert Space available in PDF, EPUB and Kindle.
