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＜電子ブック＞
Generalized B*-Algebras and Applications / by Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas
(Lecture Notes in Mathematics. ISSN:16179692 ; 2298)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XII, 241 p : online resource
著者標目	*Fragoulopoulou, Maria author Inoue, Atsushi author Weigt, Martin author Zarakas, Ioannis author SpringerLink (Online service)
件　名	LCSH:Associative rings LCSH:Associative algebras LCSH:Functional analysis LCSH:Operator theory FREE:Associative Rings and Algebras FREE:Functional Analysis FREE:Operator Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-96433-7

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