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.
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.
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
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
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