Author | Bonsall, Frank F. author |
---|---|
Title | Complete Normed Algebras [electronic resource] / by Frank F. Bonsall, John Duncan |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1973 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65669-9 |
Descript | X, 304 p. online resource |
I. Concepts and Elementary Results -- ยง 1. Normed Algebras -- ยง 2. Inverses -- ยง 3. Quasi-Inverses -- ยง 4. Equivalent Norms -- ยง 5. The Spectrum of an Element of a Complex Normed Algebra -- ยง 6. Contour Integrals -- ยง 7. A Functional Calculus for a Single Banach Algebra Element -- ยง 8. Elementary Functions -- ยง 9. Ideals and Modules -- ยง 10. The Numerical Range of an Element of a Complex Normed Algebra -- ยง 11. Approximate Identities -- ยง 12. Involutions -- ยง 13. The Complexification of a Real Algebra -- ยง 14. Normed Division Algebras -- II. Commutativity -- ยง 15. Commutative Subsets -- ยง 16. Multiplicative Linear Functionals -- ยง 17. The Gelfand Representation of a Commutative Banach Algebra -- ยง 18. Derivations and Automorphisms -- ยง 19. Generators and Joint Spectra -- ยง 20. A Functional Calculus for Several Banach Algebra Elements -- ยง 21. Functions Analytic on a Neighbourhood of the Carrier Space -- ยง 22. The Shilov Boundary -- ยง 23. The Hull-Kernel Topology -- III. Representation Theory -- ยง 24. Algebraic Preliminaries -- ยง 25. Irreducible Representations of Banach Algebras -- ยง 26. The Structure Space of an Algebra -- ยง 27. A-Module Pairings -- ยง 28. The Dual Module of a Banach Algebra -- ยง 29. The Representation of Linear Functionals -- IV. Minimal Ideals -- ยง 30. Algebraic Preliminaries -- ยง 31. Minimal Ideals in Complex Banach Algebras -- ยง 32. Annihilator Algebras -- ยง 33. Compact Action on Banach Algebras -- ยง 34. H*-Algebras -- V. Star Algebras -- ยง 35. Commutative Banach Star Algebras -- ยง 36. Continuity of the Involution -- ยง 37. Star Representations and Positive Functionals -- ยง 38. Characterizations of C*-Algebras -- ยง 39. B*-Semi-Norms -- ยง 40. Topologically Irreducible Star Representations -- ยง 41. Hermitian Algebras -- VI. Cohomology -- ยง 42. Tensor Products -- ยง 43. Amenable Banach Algebras -- ยง 44. Cohomology of Banach Algebras -- VII. Miscellany -- ยง 45. Quasi-Algebraic Elements and Capacity -- ยง 46. Nilpotents and Quasi-Nilpotents -- ยง 47. Positiveness of the Spectrum -- ยง 48. Type 0 Semi-Algebras -- ยง 49. Locally Compact Semi-Algebras -- ยง 50. Q-Algebras -- Index of Symbols