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The first unified, in-depth discussion of the now classical Gelfand-Naimark theorems, thiscomprehensive text assesses the current status of modern analysis regarding both Banachand C*-algebras.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems focuses on general theoryand basic properties in accordance with readers' needs ... provides complete proofs of theGelfand-Naimark theorems as well as refinements and extensions of the original axioms. . . gives applications of the theorems to topology, harmonic analysis. operator theory.group representations, and other topics ... treats Hermitian and symmetric *-algebras.algebras with and without identity, and algebras with arbitrary (possibly discontinuous)involutions . . . includes some 300 end-of-chapter exercises . . . offers appendices on functionalanalysis and Banach algebras ... and contains numerous examples and over 400 referencesthat illustrate important concepts and encourage further research.Characterizations of C*-Algebras: The Gelfand-Naimark Theorems is an ideal text for graduatestudents taking such courses as The Theory of Banach Algebras and C*-Algebras: inaddition , it makes an outstanding reference for physicists, research mathematicians in analysis,and applied scientists using C*-algebras in such areas as statistical mechanics, quantumtheory. and physical chemistry.
List of contents
1. The Gelfand-Naimark Theorems: Historical Perspective 2. The Gelfand-Naimark Theorem for Commutative C*-Algebras 3. The Gelfand-Naimark Theorem: Arbitrary C*-Algebras 4. Banach *-Algebras: Generalities 5. *-Representations on a Hilbert Space: A Closer Look 6. Hermitian and Symmetric *-Algebras 7. A Further Weakening of the C*-Axioms 8. Geometrical Characterizations of C*-Algebras 9. Locally C*-Equivalent Algebras 10. Applications of the Characterization Theorems
About the author
Doran\, Robert
Summary
This book gives an account of two celebrated theorems of Gelfand and Naimark for commutative C*-algebras, their tangled history, generalizations and applications, in a form accessible to mathematicians working in various applied fields, and also to students of pure and applied mathematics.
