Generalized B Algebras and Applications 1st Edition by Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas ISBN 3030964337 9783030964337

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Product details:

ISBN 10: 3030964337

ISBN 13: 978-3030964337

Author: Maria Fragoulopoulou, Atsushi Inoue, Martin Weigt, Ioannis Zarakas

Generalized B*-Algebras and Applications 1st Edition: 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.

 

Generalized B*-Algebras and Applications 1st Edition Table of contents:

• 1. Introduction
• 2. A Spectral Theory for Locally Convex Algebras
  • Basic Definitions and Notation
  • The Set of Bounded Elements. Radius of Boundedness
  • Spectrum and Spectral Radius
  • A Functional Calculus
  • The Carrier Space
• 3. Generalized B-Algebras: Functional Representation Theory
  • Hermitian and Symmetric Locally Convex *-Algebras
  • Some Results on C-Algebras
  • GB-Algebras
  • Commutative GB-Algebras: Functional Representation Theory
  • C-Like Locally Convex -Algebras as GB-Algebras
• 4. Commutative Generalized B-Algebras: Functional Calculus and Equivalent Topologies*
  • Functional Calculus
  • Positive Linear Functionals
  • Equivalent Topologies
  • A -Algebra of Functions with no GB-Topology
• 5. Extended C-Algebras and Extended W-Algebras*
  • *-Algebras and Unbounded *-Representations
  • Uniform Topologies on O-Algebras
  • Extended C-Algebras
  • Left Extended W*-Algebras of Unbounded Hilbert Algebras
• *6. Generalized B-Algebras: Unbounded -Representation Theory
  • A Functional Calculus
  • Positive Elements
  • -Representations of GB-Algebras
  • Ogasawara’s Commutativity Condition in GB-Algebras
• 7. Applications I: Miscellanea
  • The Completion of a C-Algebra Under a Locally Convex Topology
  • Continuity of Positive Linear Functionals of GB*-Algebras
  • Every GB*-Algebra has a Bounded Approximate Identity
  • Inverse Limits and Quotients of GB*-Algebras
  • A Vidav-Palmer Theorem for GB*-Algebras
• 8. Applications II: Tensor Products
  • Prerequisites: Examples
  • B-Collections in Tensor Product Locally Convex *-Algebras
  • Tensor Product GB-Algebras
  • GB-Nuclearity
  • Some Applications on Tensor Product GB*-Algebras

 

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Maria Fragoulopoulou,Atsushi Inoue,Martin Weigt,Ioannis Zarakas,Generalized,B Algebras,Applications