Ultrametric Banach algebras

Ultrametric Banach algebras / Alain Escassut.

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...

Full description

Saved in:
Bibliographic Details
Main Author: Escassut, Alain
Format: eBook
Language:English
Published: Singapore ; River Edge, NJ : World Scientific, 2003.
Subjects:
Banach algebras.
MATHEMATICS > Algebra > Linear.
Banach algebras
Algèbre de Banach.
Analyse p-adique.
Online Access:Click for online access
Table of Contents:
  • 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.

Similar Items