This book links two of the most active research areas in present day mathematics, namely Infinite Dimensional Holomorphy (on Banach spaces) and the theory of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a systematic way a wealth of recent results which are so far only accessible in research journals and contains additional original contributions. Using Banach Lie groups and Banach Lie algebras, a theory of transformation groups on infinite dimensional manifolds is presented which covers many important examples such as Grassmann manifolds and the unit balls of operator algebras. The theory also has potential importance for mathematical physics by providing foundations for the construction of infinite dimensional curved phase spaces in quantum field theory.
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978-0-08-087215-5 (9780080872155)
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Schweitzer Klassifikation
Part I. Banach Manifolds and Transformation Groups. 1. Analytic Mappings on Banach Spaces. 2. Banach Algebras. 3. Banach Manifolds. 4. Analytic Vector Fields. 5. Integration of Vector Fields. 6. Banach Lie Groups. 7. Integration of Lie Algebra Actions. 8. Submanifolds and Quotient Manifolds. 9. Binary Banach Lie Algebras. 10. Locally Uniform Transformation Groups. 11. Analytic Transformation Groups. 12. Metric and Normed Banach Manifolds. 13. Groups of Holomorphic Isometries. Part II. Symmetric Manifolds and Jordan Algebraic Structures. 14. Order Unit Banach Spaces. 15. C*-Algebras. 16. Tube Domains and Siegel Domains. 17. Symmetric Banach Manifolds. 18. Jordan Triple Systems. 19. Jordan Algebras. 20. Bounded Symmetric Domains and JB*-Triples. 21. Symmetric Siegel Domains. 22. Jordan Automorphism Groups. 23. Classical Banach Manifolds.
