An Invitation to Unbounded Representations...

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Beschreibung

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.

Über den Autor

Konrad Schmüdgen is Emeritus Professor at the Mathematical Institute of the University of Leipzig. He has worked for decades on unbounded representations and made important contributions. Among these are trace representation theorems for linear functionals, noncommutative Positivstellensätze, results on the transition probability, the theory of induced and well-behaved representations and classifications results of representations of special classes of algebras. He is the author of several books, including the Graduate Texts in Mathematics Unbounded Self-adjoint Operators on Hilbert Space (2012) and The Moment Problem (2017).

Zusammenfassung

Provides an accessible introduction to basic results and notions of unbounded representation theory

Contains an extensive study of representations of the Weyl algebra and the commutation relation of quantum mechanics

Treats many topics in unbounded representation theory in book form for the first time

Inhaltsverzeichnis

General Notation.- 1 Prologue: The Algebraic Approach to Quantum Theories.- 2 ¿-Algebras.- 3 O*-Algebras.- 4 ¿-Representations.- 5 Positive Linear Functionals.- 6 Representations of Tensor Algebras.- 7 Integrable Representations of Commutative ¿-Algebras.- 8 The Weyl Algebra and the Canonical Commutation Relation.- 9 Integrable Representations of Enveloping Algebras.- 10 Archimedean Quadratic Modules and Positivstellensätze.- 11 The Operator Relation XX*=F(X*X).- 12 Induced ¿-Representations.- 13 Well-behaved ¿-Representations.- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space.- B C*-Algebras and Representations.- C Locally Convex Spaces and Separation of Convex Sets.- References.- Symbol Index.- Subject Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xviii 381 S.
ISBN-13:	9783030463656
ISBN-10:	3030463656
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Schmüdgen, Konrad
Auflage:	1st ed. 2020
Hersteller:	Springer International Publishing Graduate Texts in Mathematics
Maße:	241 x 160 x 27 mm
Von/Mit:	Konrad Schmüdgen
Erscheinungsdatum:	28.07.2020
Gewicht:	0,764 kg

Artikel-ID: 118124813