TY  - BOOK
AU  - Murphy,Gerard J.
TI  - C*-algebras and operator theory
SN  - 9780080924960
AV  - QA326 .M87 1990eb
U1  - 512/.55 22
PY  - 1990///
CY  - Boston
PB  - Academic Press
KW  - C*-algebras
KW  - Operator theory
KW  - C*-alg�ebres
KW  - Op�erateurs, Th�eorie des
KW  - MATHEMATICS
KW  - Algebra
KW  - Intermediate
KW  - bisacsh
KW  - fast
KW  - C-Stern-Algebra
KW  - gnd
KW  - Operatortheorie
KW  - C
KW  - alg�ebres
KW  - ram
KW  - Op�erateurs, th�eorie des
KW  - Electronic books
N1  - Includes bibliographical references (page 279.280) and index; 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
N2  - 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 prior acquaintance with operator theory is required
UR  - https://www.sciencedirect.com/science/book/9780080924960
ER  -