Buch, Englisch, 168 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 423 g
Buch, Englisch, 168 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 423 g
Reihe: Studies in Advanced Mathematics
ISBN: 978-0-8493-7875-1
Verlag: CRC Press
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.
Zielgruppe
Professional
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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
