Complete Normed Algebras

Complete Normed Algebras by Frank F. Bonsall, John Duncan.

The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, m...

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Bibliographic Details
Main Authors: Bonsall, Frank F. (Author), Duncan, John (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1973.
Edition:1st ed. 1973.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics ; 80
Springer eBook Collection.
Subjects:
Matrix theory.
Algebra.
Operator theory.
Functional analysis.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. Concepts and Elementary Results
  • § 1. Normed Algebras
  • § 2. Inverses
  • § 3. Quasi-Inverses
  • § 4. Equivalent Norms
  • § 5. The Spectrum of an Element of a Complex Normed Algebra
  • § 6. Contour Integrals
  • § 7. A Functional Calculus for a Single Banach Algebra Element
  • § 8. Elementary Functions
  • § 9. Ideals and Modules
  • § 10. The Numerical Range of an Element of a Complex Normed Algebra
  • § 11. Approximate Identities
  • § 12. Involutions
  • § 13. The Complexification of a Real Algebra
  • § 14. Normed Division Algebras
  • II. Commutativity
  • § 15. Commutative Subsets
  • § 16. Multiplicative Linear Functionals
  • § 17. The Gelfand Representation of a Commutative Banach Algebra
  • § 18. Derivations and Automorphisms
  • § 19. Generators and Joint Spectra
  • § 20. A Functional Calculus for Several Banach Algebra Elements
  • § 21. Functions Analytic on a Neighbourhood of the Carrier Space
  • § 22. The Shilov Boundary
  • § 23. The Hull-Kernel Topology
  • III. Representation Theory
  • § 24. Algebraic Preliminaries
  • § 25. Irreducible Representations of Banach Algebras
  • § 26. The Structure Space of an Algebra
  • § 27. A-Module Pairings
  • § 28. The Dual Module of a Banach Algebra
  • § 29. The Representation of Linear Functionals
  • IV. Minimal Ideals
  • § 30. Algebraic Preliminaries
  • § 31. Minimal Ideals in Complex Banach Algebras
  • § 32. Annihilator Algebras
  • § 33. Compact Action on Banach Algebras
  • § 34. H*-Algebras
  • V. Star Algebras
  • § 35. Commutative Banach Star Algebras
  • § 36. Continuity of the Involution
  • § 37. Star Representations and Positive Functionals
  • § 38. Characterizations of C*-Algebras
  • § 39. B*-Semi-Norms
  • § 40. Topologically Irreducible Star Representations
  • § 41. Hermitian Algebras
  • VI. Cohomology
  • § 42. Tensor Products
  • § 43. Amenable Banach Algebras
  • § 44. Cohomology of Banach Algebras
  • VII. Miscellany
  • § 45. Quasi-Algebraic Elements and Capacity
  • § 46. Nilpotents and Quasi-Nilpotents
  • § 47. Positiveness of the Spectrum
  • § 48. Type 0 Semi-Algebras
  • § 49. Locally Compact Semi-Algebras
  • § 50. Q-Algebras
  • Index of Symbols.

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