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Ultrametric Banach algebras /
In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
2003.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Basic properties in commutative algebra
- 2. Tree structure
- 3. Ultrametric absolute values
- 4. L-productal vector spaces
- 5. Multiplicative semi-norms and Shilov boundary
- 6. Spectral semi-norm
- 7. Hensel Lemma
- 8. Infraconnected sets
- 9. Monotonous filters
- 10. Circular filters
- 11. Tree structure and metric on circular filters
- 12. Rational functions and algebras R(D)
- 13. Simple convergence on Mult(K[x])
- 14. Topologies on Mult(K[x])
- 15. Spectral properties and Gelfand transforms
- 16. Analytic elements
- 17. Holomorphic properties on infraconnected sets
- 18. T-filters and T-sequences
- 19. Applications of T-filters and T-sequences
- 20. Analytic elements on classic partitions
- 21. Holomorphic properties on partitions
- 22. Shilov boundary for algebras H(D, O)
- 23. Holomorphic functional calculus
- 24. Uniform K-Banach algebras and properties (s) and (q)
- 25. Properties (o) and (q) in uniform Banach K-algebras
- 26. Properties (o) and (q) and strongly valued fields
- 27. Multbijective Banach K-algebras
- 28. Pseudo-density of Mult[symbol]
- 29. Polnorm on algebras and algebraic extensions
- 30. Definition of affinoid algebras
- 31. Algebraic properties of affinoid algebras
- 32. Jacobson radical of affinoid algebras
- 33. Salmon's theorems
- 34. Separable fields
- 35. Spectral norm of affinoid algebras
- 36. Spectrum of an element of an affinoid algebra
- 37. Krasner-Tate algebras
- 38. Universal generators in Tate algebras
- 39. Mappings from H(D) to the tree Mult(K[x])
- 40. Continuous mappings on Mult(K[x])
- 41. Examples and counterexamples
- 41. Associated idempotents
- 43. Krasner-Tate algebras among Banach K-algebras.