Theory of Operator Algebras I
Springer-Verlag New York Inc.
978-1-4612-6190-2 (ISBN)
I Fundamentals of Banach Algebras and C*-Algebras.- 0. Introduction.- 1. Banach Algebras.- 2. Spectrum and Functional Calculus.- 3. Gelfand Representation of Abelian Banach Algebras.- 4. Spectrum and Functional Calculus in C*-Algebras.- 5. Continuity of Homomorphisms.- 6. Positive Cones of C*-Algebras.- 7. Approximate Identities in C*-Algebras.- 8. Quotient Algebras of C*-Algebras.- 9. Representations and Positive Linear Functional.- 10. Extreme Points of the Unit Ball of a C*-Algebra.- 11. Finite Dimensional C*-Algebras.- Notes.- Exercises.- II Topologies and Density Theorems in Operator Algebras.- 0. Introduction.- 1. Banach Spaces of Operators on a Hilbert Space.- 2. Locally Convex Topologies in ?(?).- 3. The Double Commutation Theorem of J. von Neumann.- 4. Density Theorems.- Notes.- III Conjugate Spaces.- 0. Introduction.- 1. Abelian Operator Algebras.- 2. The Universal Enveloping von Neumann Algebra of a C*-Algebra.- 3. W*-Algebras.- 4. The Polar Decomposition and the Absolute Value of Functionals.- 5. Topological Properties of the Conjugate Space.- 6. Semicontinuity in the Universal Enveloping von Neumann Algebra*.- Notes.- IV Tensor Products of Operator Algebras and Direct Integrals.- 0. Introduction.- 1. Tensor Product of Hilbert Spaces and Operators.- 2. Tensor Products of Banach Spaces.- 3. Completely Positive Maps.- 4. Tensor Products of C*-Algebras.- 5. Tensor Products of W*-Algebras.- Notes.- 6. Integral Representations of States.- 7. Representation of L2(?,?) ? ?, L1(?,?) ?y? *, and L(?,?) ?? ?.- 8. Direct Integral of Hubert Spaces, Representations, and von Neumann Algebras.- Notes.- V Types of von Neumann Algebras and Traces.- 0. Introduction.- 1. Projections and Types of von Neumann Algebras.- 2. Traces on von Neumann Algebras.-Notes.- 3. Multiplicity of a von Neumann Algebra on a Hilbert Space.- 4. Ergodic Type Theorem for von Neumann Algebras*.- 5. Normality of Separable Representations*.- 6. The Borel Spaces of von Neumann Algebras.- 7. Construction of Factors of Type II and Type III.- Notes.- Appendix Polish Spaces and Standard Borel Spaces.- Monographs.- Papers.- Notation Index.
Erscheint lt. Verlag | 5.11.2011 |
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Zusatzinfo | VIII, 418 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
Medizin / Pharmazie | |
Schlagworte | Algebras • Analysis • Operator • Operatoralgebra |
ISBN-10 | 1-4612-6190-2 / 1461261902 |
ISBN-13 | 978-1-4612-6190-2 / 9781461261902 |
Zustand | Neuware |
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