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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 |
MARC
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| 100 | 1 | |a Escassut, Alain. | |
| 245 | 1 | 0 | |a Ultrametric Banach algebras / |c Alain Escassut. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c 2003. | ||
| 300 | |a 1 online resource (xiii, 275 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references (pages 265-267) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A. | ||
| 505 | 0 | |a 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. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Banach algebras. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Banach algebras. |2 fast |0 (OCoLC)fst00826385 | |
| 650 | 1 | 7 | |a Algèbre de Banach. |2 rasuqam |
| 650 | 7 | |a Analyse p-adique. |2 rasuqam | |
| 776 | 0 | 8 | |i Print version: |a Escassut, Alain. |t Ultrametric Banach algebras. |d Singapore ; River Edge, NJ : World Scientific, 2003 |z 9812381945 |z 9789812381941 |w (OCoLC)52425467 |
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