Generalized B*-Algebras and Applications

Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas (Autoren)

Buch | Softcover

XII, 241 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-030-96432-0 (ISBN)

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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.

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.

"This book deals with the theory of locally convex algebras, in general, and of generalized

B_-algebras (GB_-algebras in short) in particular. It is well written and self-contained." (Lahbib Oubbi, Mathematical Reviews, November, 2023)
"The book has been written by specialists that are actively working in the field. The choice of the presented material has been done with great care. The bibliography contains all classical monographs, all important papers, and most recent ones. The book leads the reader 'smoothly' ... . It will therefore serve as an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field." (Andrzej Soltysiak, zbMATH 1498.46001, 2022)

“The book has been written by specialists that are actively working in the field. The choice of the presented material has been done with great care. The bibliography contains all classical monographs, all important papers, and most recent ones. The book leads the reader 'smoothly' ... . It will therefore serve as an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.” (Andrzej Sołtysiak, zbMATH 1498.46001, 2022)

Erscheinungsdatum	12.06.2022
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 241 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	396 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Extended C-Algebras • Extended W-Algebras • functional calculus • Generalized B-Algebras • spectral theory • Unbounded -Representations
ISBN-10	3-030-96432-9 / 3030964329
ISBN-13	978-3-030-96432-0 / 9783030964320
Zustand	Neuware