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Generalized B*-Algebras and Applications (Paperback, 1st ed. 2022)
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Generalized B*-Algebras and Applications (Paperback, 1st ed. 2022)
Series: Lecture Notes in Mathematics, 2298
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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.
General
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