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Theory of Operator Algebras I

Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda­...

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Bibliographic Details
Main Author: Takesaki, Masamichi
Format: eBook
Language:English
Published: New York, NY Springer New York 1979, 1979
Edition:1st ed. 1979
Subjects:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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

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