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Generalized B*-Algebras and Applications

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Generalized B*-Algebras and Applications/ by Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas.
Author:	Fragoulopoulou, Maria.
other author:	Inoue, Atsushi.
Description:	XII, 241 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Associative rings. -
Online resource:	https://doi.org/10.1007/978-3-030-96433-7
ISBN:	9783030964337

Generalized B*-Algebras and Applications
Fragoulopoulou, Maria.

Generalized B*-Algebras and Applications[electronic resource] /by Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas. - 1st ed. 2022. - XII, 241 p.online resource. - Lecture Notes in Mathematics,22981617-9692 ;. - Lecture Notes in Mathematics,2144.

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 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.

ISBN: 9783030964337

Standard No.: 10.1007/978-3-030-96433-7doiSubjects--Topical Terms:

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Generalized B*-Algebras and Applications
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505 0 $a 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.
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