Fundamentals of the Theory of Operator Algebras

1. Front Matter

   Pages i-xiv

   PDF

2. Comparison Theory of Projections

   • Richard V. Kadison, John R. Ringrose

   Pages 274-311

3. Normal States and Unitary Equivalence of Von Neumann Algebras

   • Richard V. Kadison, John R. Ringrose

   Pages 312-367

4. The Trace

   • Richard V. Kadison, John R. Ringrose

   Pages 368-450

5. Algebra and Commutant

   • Richard V. Kadison, John R. Ringrose

   Pages 451-545

6. Special Representations of C*-Algebras

   • Richard V. Kadison, John R. Ringrose

   Pages 546-679

7. Tensor Products

   • Richard V. Kadison, John R. Ringrose

   Pages 680-725

8. Approximation by Matrix Algebras

   • Richard V. Kadison, John R. Ringrose

   Pages 726-782

9. Crossed Products

   • Richard V. Kadison, John R. Ringrose

   Pages 783-817

10. Direct Integrals and Decompositions

    • Richard V. Kadison, John R. Ringrose

    Pages 818-841

11. Back Matter

    Pages 842-859

    PDF

These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub­ ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer­ cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at­ tentive, diligent, well-motivated reader.

• C*-algebra
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• algebra
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• Department of Mathematics, University of Pennsylvania, Philadelphia, USA

  Richard V. Kadison

• School of Mathematics, University of Newcastle, Newcastle upon Tyne, England

  John R. Ringrose

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