Kehe Zhu

An Introduction to Operator Algebras (eBook, PDF)

• Format: PDF

Produktbeschreibung

An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 176
• Erscheinungstermin: 11. Mai 2018
• Englisch
• ISBN-13: 9781351467032
• Artikelnr.: 56887730

Autorenporträt

Zhu, Kehe

Inhaltsangabe

Preface
I. Banach Algebras
1. Review on Functional Analysis
2. Banach Algebras and the Invertible Group
3. The Spectrum
4. Multiplicative Linear Functionals
5. The Gelfand Transform and Applications
6. Examples of Maximal Ideal Spaces
7. Non-Unital Banach Algebras
II. C*-Algebras
8. C*-Algebras
9. Commutative C*-Algebras
10. The Spectral Theorem and Applications
11. Further Applications
12. Polar Decomposition
13. Positive Linear Functionals and States
14. The GNS Construction
15. Non-Unital C*-Algebras
III. Von Neumann Algebras
16. Strong- and Weak-Operator Topologies
17. Existence of Projections
18. The Double Commutant Theorem
19. The Kaplansky Density Theorem
20. The Borel Functional Calculus
21. L°° as a von Neumann Algebra
22. Abelian von Neumann Algebras
23. The -Functional Calculus
24. Equivalence of Projections
25. A Partial Ordering
26. Type Decomposition
Bibliography
Index