Unbounded Operator Algebras and Representation 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 Unbounded Operator Algebras and Representation Theory write by K. Schmüdgen. This book was released on 2013-11-11. Unbounded Operator Algebras and Representation Theory available in PDF, EPUB and Kindle. *-algebras of unbounded operators in Hilbert space, or more generally algebraic systems of unbounded operators, occur in a natural way in unitary representation theory of Lie groups and in the Wightman formulation of quantum field theory. In representation theory they appear as the images of the associated representations of the Lie algebras or of the enveloping algebras on the Garding domain and in quantum field theory they occur as the vector space of field operators or the *-algebra generated by them. Some of the basic tools for the general theory were first introduced and used in these fields. For instance, the notion of the weak (bounded) commutant which plays a fundamental role in thegeneraltheory had already appeared in quantum field theory early in the six ties. Nevertheless, a systematic study of unbounded operator algebras began only at the beginning of the seventies. It was initiated by (in alphabetic order) BORCHERS, LASSNER, POWERS, UHLMANN and VASILIEV. J1'rom the very beginning, and still today, represen tation theory of Lie groups and Lie algebras and quantum field theory have been primary sources of motivation and also of examples. However, the general theory of unbounded operator algebras has also had points of contact with several other disciplines. In particu lar, the theory of locally convex spaces, the theory of von Neumann algebras, distri bution theory, single operator theory, the momcnt problem and its non-commutative generalizations and noncommutative probability theory, all have interacted with our subject.
Unbounded Operator Algebras and Representation Theory
Unbounded Operator Algebras and Representation 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 Unbounded Operator Algebras and Representation Theory write by Konrad Schmüdgen. This book was released on 1990. Unbounded Operator Algebras and Representation Theory available in PDF, EPUB and Kindle.
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
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.
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 2021-03-01. 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-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.
