C*-Algebras and W*-Algebras / by Shoichiro Sakai.

Author
In
  • Springer eBooks
Other titles
  • Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 60
Edition
  • 1st ed. 1998.
Published
  • Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer 1998
Physical description
1 online resource (XII, 259 p.)
ISBN
  • 3-642-61993-2
Notes
  • "Reprint of the 1971 Edition."
  • Includes bibliographical references and index.
  • English
Contents
  • 1. 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 Self-Adjoint 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. Radon-Nikodym 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 (Non-Separable Cases) -- 3.2. Reduction Theory (Space-Free) -- 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 (Non-Factors) -- 4.6. Type I C*-Algebras -- 4.7. On a Stone-Weierstrass Theorem for C*-Algebras -- List of Symbols.
Related item
Genre
  • text
Language
  • English

Summary

  • 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 well-trained third-year 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).

Summary holdings does not include live availability details. Select a library name for the full Holdings display.

Location of copy Shelfmark Online location Holdings Notes
University of Bath Library Online location
University of Bath Library Online location
University of Bath Library Online location
British Library: Science, Technology and Industry, St Pancras Reading Rooms RES (B) PC 54
British Library: Lending Collection 3807.180000 v.60
University of Cambridge Libraries: University Library: South Front, Floor 4 348:01.c.3.45
University of Cambridge Libraries: Moore Library: Main Library QA326 .S25 1971
University of Cambridge Libraries: Moore Library: Main Library QA326 .S25 1998
Cardiff University Libraries Online location
Durham University Library: Bill Bryson Library, Level 3 510 ERG (60)
University of Edinburgh Libraries: Murray Library, King's Buildings (STANDARD LOAN) QA326 Sak.
University of Exeter Library: Old Library 512.55 SAK
University of Glasgow Library: University Library Level 5 Mathematics 4665 1971-S
Imperial College London Library: Central Library: Level 2 517.986.32 SAK
King's College London Library: Maughan Library ; [Science books] QA326 Sa28,Sa29 Four week
University of Liverpool Library: Harold Cohen Library, Ground Floor Rear (Book Zone 3) QA326.S15 0
Newcastle University Libraries: Philip Robinson Library: Robinson Books Level 3 512.556 SAK
University of Nottingham Libraries: George Green Library
Open University Library: First Floor Open Shelves 512.55
University of Oxford Libraries: Mathematical Institute Library 46
University of Oxford Libraries: Mathematical Institute Library 46
University of Oxford Libraries: Radcliffe Science Library
University of Oxford Libraries: Wadham College Library M 18 (S)
University of Oxford Libraries: St Anne's College Library: Tim Gardam Building 512.6 SAK:C*-
University of Oxford Libraries: St Hilda's College Library 510.2 SAK:Alg
University of Oxford Libraries: Somerville College Library 512 SAK 1
University of Oxford Libraries: Wolfson College Library: Floersheimer 512.55 SAK
Queen Mary University of London Library: Mile End Library QA326 SAK (ORDINARY) ORDINARY
University of Reading Library: University Library: Off-site Store - available on request STORE--04271
University of St Andrews Library: J F Allen Library QA3.E8;60 per
Science Museum Library: Science Museum Library, Wroughton 517.98 SAKAI
University of Southampton Library: Hartley Library QA 253 SAK
University of Surrey Online location
Trinity College Dublin Library: Contact Trinity College Library Dublin Mathematics Department
UCL Library Services: UCL Science Library MATHEMATICS K 80 SAK
University of Warwick Library: External Store QA 326.S2
University of Warwick Library: Maths Institute QA 326.S2
University of Warwick Library: Maths Institute QA 326.S2
University of Warwick Library Online location Connect to Springer e-book

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