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C*algebras and W*algebras
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Classics in Mathematics
By
Shoichiro Sakai
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Rating:   Format:  Paperback, 271 pages, Reprint of the 1st e Edition  Other Information:  biography  Published In:  Germany, 11 December 1997 
From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." (Math. Reviews) "In theory, this book can be read by a welltrained thirdyear graduate student  but the reader had better have a great deal of mathematical sophistication. The specialist in this and allied areas will find the wealth of recent results and new approaches throughout the text especially rewarding." (American Scientist) "The title of this book at once suggests comparison with the two volumes of Dixmier and the fact that one can seriously make this comparison indicates that it is a far more substantial work that others on this subject which have recently appeared"(BLMSoc) Table of Contents1. General Theory. 1.1. Definitions of C*Algebras and W*Algebras. 1.2. Commutative C*Algebras. 1.3. Stonean Spaces. 1.4. Positive Elements of a C*Algebra. 1.5. Positive Linear Functionals on a C*Algebra. 1.6. Extreme Points in the Unit Sphere of a C*Algebra. 1.7. The Weak Topology on a W*Algebra. 1.8. Various Topologies on a W*Algebra. 1.9. Kaplansky's Density Theorem. 1.10. Ideals in a W*Algebra. 1.11. Spectral Resolution of SelfAdjoint Elements in a W*Algebra. 1.12. The Polar Decomposition of Elements of a W*Algebra. 1.13. Linear Functionals on a W*Algebra. 1.14. Polar Decomposition of Linear Functionals on a W*Algebra. 1.15. Concrete C*Algebras and W*Algebras. 1.16. The Representation Theorems for C*Algebras and W* Algebras. 1.17. The Second Dual of a C*Algebra. 1.18. Commutative W*Algebras. 1.19. The C*Algebra C(?) of all Compact Linear Operators on a Hilbert Space ?. 1.20. The Commutation Theorem of von Neumann. 1.21. *Representations of C*Algebras, 1. 1.22. Tensor Products of C*Algebras and W*Algebras. 1.23. The Inductive Limit and Infinite Tensor Product of C* Algebras. 1.24. RadonNikodym Theorems in W*Algebras. 2. Classification of W*Algebras. 2.1. Equivalence of Projections and the Comparability Theorem. 2.2. Classification of W*Algebras. 2.3. Type I W*Algebras. 2.4. Finite W*Algebras. 2.5. Traces and Criterions of Types. 2.6. Types of Tensor Products of W*Algebras. 2.7. *Representations of C*Algebras and W*Algebras, 2. 2.8. The Commutation Theorem of Tensor Products. 2.9. Spatial Isomorphisms of W*Algebras. 3. Decomposition Theory. 3.1. Decompositions of States (NonSeparable Cases). 3.2. Reduction Theory (SpaceFree). 3.3. Direct Integral of Hilbert Spaces. 3.4. Decomposition of States (Separable Cases). 3.5. Central Decomposition of States (Separable Cases). 4. Special Topics. 4.1. Derivations and Automorphisms of C*Algebras and W*Algebras. 4.2. Examples of Factors, 1 (General Construction). 4.3. Examples of Factors, 2 (Uncountable Families of Types II 1, II? and III. 4.4. Examples of Factors, 3 (Other Results and Problems). 4.5. Global W*Algebras (NonFactors). 4.6. Type I C*Algebras. 4.7. On a StoneWeierstrass Theorem for C*Algebras. List of Symbols. Promotional InformationSpringer Book Archives EAN: 
9783540636335 

ISBN: 
3540636331 

Publisher: 
SpringerVerlag Berlin and Heidelberg GmbH & Co. K 

Dimensions: 
23.4 x 15.6 x 1.4 centimeters (0.51 kg) 

Age Range: 
15+ years 

