Fragoulopoulou / Inoue / Weigt Generalized B*-Algebras and Applications

Erscheinungsjahr 2022
ISBN: 978-3-030-96433-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 241 Seiten

Reihe: Mathematics and Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Fragoulopoulou, Maria

Inoue, Atsushi

Weigt, Martin

Zarakas, Ioannis

Inhaltsverzeichnis

1. Introduction.- 2. A Spectral Theory for Locally Convex Algebras.- 3. Generalized B*-Algebras: Functional Representation Theory.- 4. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.- 5. Extended C*-Algebras and Extended W*-Algebras.- 6. Generalized B*-Algebras: Unbounded *-Representation Theory.- 7. Applications I: Miscellanea.- 8. Applications II: Tensor Products.