C*-algebras and operator theory /

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no p...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Murphy, Gerard J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston : Academic Press, �1990.
Temas:
C*-algebras.
Operator theory.
C*-alg�ebres.
Th�eorie des op�erateurs.
MATHEMATICS > Algebra > Intermediate.
C-Stern-Algebra
Operatortheorie
C > alg�ebres.
Op�erateurs, th�eorie des.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover ; C*-Algebras and Operator Theory; Copyright Page; Table of Contents; Preface; Chapter 1. Elementary Spectral Theory; 1.1. Banach Algebras; 1.2. The Spectrum and the Spectral Radius; 1.3. The Gelfand Representation; 1.4. Compact and Fredholm Operators; Exercises; Addenda; Chapter 2. C*-Algebras and Hilbert Space Operators; 2.1. C*-Algebras; 2.2. Positive Elements of C*-Algebras; 2.3. Operators and Sesquilinear Forms; 2.4. Compact Hilbert Space Operators; 2.5. The Spectral Theorem; Exercises; Addenda; Chapter 3. Ideals and Positive Functionals; 3.1. Ideals in C*-Algebras.
  • 3.2. Hereditary C*-Subalgebras3.3. Positive Linear Functionals; 3.4. The Gelfand-Naimark Representation; 3.5. Toeplitz Operators; Exercises; Addenda; Chapter 4. Von Neumann Algebras; 4.1. The Double Commutant Theorem; 4.2. The Weak and Ultraweak Topologies; 4.3. The Kaplansky Density Theorem; 4.4. Abelian Von Neumann Algebras; Exercises; Addenda; Chapter 5. Representations of C*-Algebras; 5.1. Irreducible Representations and Pure States; 5.2. The Transitivity Theorem; 5.3. Left Ideals of C*-Algebras; 5.4. Primitive Ideals; 5.5. Extensions and Restrictions of Representations.
  • 5.6. Liminal and Postliminal C*-AlgebrasExercises; Addenda; Chapter 6. Direct Limits and Tensor Products; 6.1. Direct Limits of C*-Algebras; 6.2. Uniformly Hyperfinite Algebras; 6.3. Tensor Products of C*-Algebras; 6.4. Minimality of the Spatial C*-Norm; 6.5. Nuclear C*-Algebras and Short Exact Sequences; Exercises; Addenda; Chapter 7. K-Theory of C*-Algebras; 7.1. Elements of K-Theory; 7.2. The K-Theory of AF-Algebras; 7.3. Three Fundamental Results in K-Theory; 7.4. Stability; 7.5. Bott Periodicity; Exercises; Addenda; Appendix; Notes; References; Notation Index; Subject Index.

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