Generalized B*-Algebras and Applications

Download or read book Generalized B*-Algebras and Applications written by Maria Fragoulopoulou and published by Springer Nature. This book was released on 2022-06-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.