TY  - BOOK
AU  - Schmüdgen, Konrad
TI  - Invitation to unbounded representations of *- algebras on hilbert space
T2  - Graduate texts in mathematics ; 
SN  - 9783030463687
U1  - 512.5 
PY  - 2020///
CY  - Cham, Switzerland : 
PB  - Springer
KW  - Associative rings and algebras
KW  - Hilbert algebras
KW  - Hilbert space
KW  - Lie groups
KW  - Operator algebras
KW  - Operator theory
KW  - Topological Groups, Lie Groups
KW  - Trace functionals
KW  - Unbounded representations
KW  - Quadratic modules
KW  - Infinitesimal representations
KW  - Weyl algebra
N1  - Includes bibliographical references and index
N2  - 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
UR  - https://link.springer.com/content/pdf/bfm:978-3-030-46366-3/1
UR  - https://www.goodreads.com/book/show/72499137-an-invitation-to-unbounded-representations-of--algebras-on-hilbert-spac?ac=1&from_search=true&qid=oHHw0TYwL9&rank=1#CommunityReviews
ER  -