Title | Theory of Operator Algebras I [electronic resource] / edited by Masamichi Takesaki |
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Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6188-9 |
Descript | VIII, 418 p. online resource |
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