Skip to main content

Elements for a classification of commutative radical Banach algebras

I. General Theory Of Radical Banach Algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 975)

Keywords

  • Prime Ideal
  • Nonzero Element
  • Banach Algebra
  • Integral Domain
  • Principal Ideal

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. R. Allan, Embedding the algebra of all formal power series in a Banach algebra, Proc. London Math. Soc., (3) 25 (1972), 329–340.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. _____, Elements of finite closed descent in a Banach algebra, J. London Math. Soc., 7 (1973), 462–466.

    MathSciNet  MATH  Google Scholar 

  3. G. R. Allan and A. M. Sinclair, Power factorization in Banach algebras with a bounded approximate identity, Studia Math., 56 (1976), 31–38.

    MathSciNet  MATH  Google Scholar 

  4. M. Altman, Contracteurs dans les algèbres de Banach, C. R. Acad. Sci. Paris, Ser. AB, 272 (1971), 1388–1389.

    MathSciNet  MATH  Google Scholar 

  5. W. G. Bade, P. C. Curtis, Jr. and K. B. Laursen, Divisible subspaces and problems in automatic continuity, Studia Math., 48 (1980), 159–186.

    MathSciNet  MATH  Google Scholar 

  6. W. G. Bade and H. G. Dales, Norms and ideals in radical convolution algebras, J. Functional Analysis, 41 (1981), 77–109.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. R. P. Boas, Entire Functions, Academic Press, New York, 1954.

    MATH  Google Scholar 

  8. H. Bohr, Almost Periodic Functions, Chelsea Publishing Company, New York (1947).

    MATH  Google Scholar 

  9. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, Berlin, Heidelberg, New York, 1973.

    CrossRef  MATH  Google Scholar 

  10. S. H. Bouloussa, Caracterisation des algèbres de Fréchet qui sont des anneaux de valuation, J. London Math. Soc., (2) 25 (1982), 355–364.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. N. Bourbaki, Topologie Générale, Chapitre II, Hermann, Paris, 1960.

    Google Scholar 

  12. P. J. Cohen, Factorization in group algebras, Duke Math. J., 26 (1959), 199–206.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. H. G. Dales, A discontinuous homomorphism from C(X), Amer. J. Math., 101 (1979), 647–734.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. _____, Convolution algebras on the real line, this Volume.

    Google Scholar 

  15. _____, Automatic continuity: a survey, Bull. London Math. Soc., 10 (1978), 129–183.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Y. Domar, A solution of the translation-invariant subspace problem for weighted LP on ℝ, ℝ+ or ℤ, This Volume.

    Google Scholar 

  17. J. Esterle, Solution d'un problème d'Erdös, Gillman et Henriksen et application à l'étude des homomorphismes de C(K), Acta Math., (Hungarica), 30 (1977), 113–127.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. _____, Sur l'existence d'un homomorphisme discontinu de C(K), Proc. London Math. Soc., (3) 36 (1978), 46–58.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, Injection de semigroupes divisibles dans des algèbres de convolution et construction d'homomorphismes discontinus de C(K), Proc. London Math. Soc., (3) 36 (1978), 59–85.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____, Homomorphismes discontinus des algèbres de Banach commutatives separables, Studia Math., 66 (1979), 119–141.

    MathSciNet  MATH  Google Scholar 

  21. _____, Rates of decrease of sequences of powers in commutative radical Banach algebras, Pacific J. Math., 94 (1981), 61–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. _____, Theorems of Gelfand-Mazur type and continuity of epimorphisms from C(K), J. Functional Analysis, 36 (1980), 273–286.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. _____, Universal properties of some commutative radical Banach algebras, J. für die Reine und ang. Math., 321 (1981), 1–24.

    MathSciNet  MATH  Google Scholar 

  24. _____, A complex variable proof of the Wiener Tauberian theorem, Ann. Inst. Fourier, (2) 30 (1980), 91–96.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. _____, Irregularity of the rate of decrease of sequences of powers in the Volterra algebra, Canad. J. Math., 33 (1981), 320–324.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. _____, Quasimultipliers, representations of H, and the closed ideal problem for commutative Banach algebras, this Volume.

    Google Scholar 

  27. S. Grabiner, Derivations and automorphisms of Banach algebras of power series, Memoris Amer. Math. Soc., 146 (1975).

    Google Scholar 

  28. N. Grønbaek, Power factorization in Banach modules over commutative radical Banach algebras, Math. Scand., 50 (1982), 123–134.

    MathSciNet  MATH  Google Scholar 

  29. E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Colloquium Publication Series, Vol. 31, Amer. Math. Soc., Providence, Rhode Island, 1957.

    MATH  Google Scholar 

  30. K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962.

    MATH  Google Scholar 

  31. B. E. Johnson, Continuity of centralizers on Banach algebras, J. London Math. Soc., 41 (1966), 639–640.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. K. Kuratowski, Topology, Vol. I, Academic Press, New York and London, 1966.

    MATH  Google Scholar 

  33. B. J. Levin, Distribution of Zeros of Entire Functions, Translations of Math. Monographs, Vol. 5, revised edition, Amer. Math. Soc., Providence, Rhode Island, 1964.

    MATH  Google Scholar 

  34. B. Nyman, On the one dimensional translation group on certain function spaces, Thesis, Uppsala (1950).

    Google Scholar 

  35. C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, New Jersey, 1960.

    MATH  Google Scholar 

  36. A. M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Functional Analysis, 29 (1978), 308–318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  37. _____, Continuous Semigroups in Banach Algebras, London Math. Soc. Lecture Notes, 63, Cambridge University Press, 1982.

    Google Scholar 

  38. M. P. Thomas, Algebra homomorphisms and the functional calculus, Pacific J. Math., 79 (1978), 251–269.

    CrossRef  MathSciNet  MATH  Google Scholar 

  39. N. T. Varopoulos, Continuité des formes linéaires positives sur une algèbre de Banach avec involution, C. R. Acad. Sci. Paris, Ser. AB 258 (1964), 1121–1124.

    MathSciNet  MATH  Google Scholar 

  40. F. Zouakia, The theory of Cohen elements, this Volume.

    Google Scholar 

  41. _____, Semigroupes réels dans certaines algèbres de Banach commutatives radicales, Thèse de 3e cycle, Bordeaux, Juin 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Esterle, J. (1983). Elements for a classification of commutative radical Banach algebras. In: Bachar, J.M., Bade, W.G., Curtis, P.C., Dales, H.G., Thomas, M.P. (eds) Radical Banach Algebras and Automatic Continuity. Lecture Notes in Mathematics, vol 975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064547

Download citation

  • DOI: https://doi.org/10.1007/BFb0064547

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11985-2

  • Online ISBN: 978-3-540-39454-9

  • eBook Packages: Springer Book Archive