Complete Normed Algebras

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Product Details

  • ISBN-13: 9783540063865
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 12/28/1973

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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