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 2021-03-01. 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.
Tomita's Theory of Modular Hilbert Algebras and its Applications
Tomita's Theory of Modular Hilbert Algebras and its 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 Tomita's Theory of Modular Hilbert Algebras and its Applications write by M. Takesaki. This book was released on 2006-11-15. Tomita's Theory of Modular Hilbert Algebras and its Applications available in PDF, EPUB and Kindle.
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-Takesaki Theory in Algebras of Unbounded Operators
Tomita-Takesaki Theory in Algebras of Unbounded Operators - 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-Takesaki Theory in Algebras of Unbounded Operators write by Atsushi Inoue. This book was released on 2006-11-14. Tomita-Takesaki Theory in Algebras of Unbounded Operators available in PDF, EPUB and Kindle. These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.
A Primer on Hilbert Space Theory
A Primer on Hilbert Space Theory - 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 A Primer on Hilbert Space Theory write by Carlo Alabiso. This book was released on 2021-03-03. A Primer on Hilbert Space Theory available in PDF, EPUB and Kindle. This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
