Skip to main content

Quasimultipliers, representations of H, and the closed ideal problem for commutative Banach algebras

  • I. General Theory Of Radical Banach Algebras
  • Conference paper
  • First Online:

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

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (USA)
  • 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. M. Akkar, Etude spectrale et structure des algèbres topologiques et bornologiques complètes, Thèse de Doctorat d'Etat de Mathématiques, Bordeaux, 1976.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  3. Ideals of rapidly growing functions, Proceedings International Symposium on functional analysis and its applications, Ibadan, Nigeria (1977), 85–109.

    Google Scholar 

  4. G. R. Allan, H. G. Dales and J. P. McClure, Pseudo-Banach algebras, Studia Math., 40 (1971), 55–69.

    MathSciNet  MATH  Google Scholar 

  5. M. Altman, Contracteurs dans les algèbres de Banach, C. R. Acad. Sci. Paris Ser A-B, 274 (1972), 399–400.

    MathSciNet  MATH  Google Scholar 

  6. C. Apostol, Functional calculus and invariant subspaces, J. Operator Theory, 4 (1980), 159–190.

    MathSciNet  MATH  Google Scholar 

  7. A. Atzmon, Operators which are annihilated by analytic functions and invariant subspaces, Acta Math., 144 (1980), 27–63.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Beauzamy, Sous espaces invariants de type fonctionnel dans les espaces de Banach, Acta Math., 144 (1980), 65–82.

    Article  MathSciNet  MATH  Google Scholar 

  10. _____, Sous espaces invariants dans les espaces de Banach, Seminaire N. Bourbaki, 549, (Fevrier, 1980).

    Google Scholar 

  11. M. Berkani, Inegalités dans les algèbres de Banach et proprietés spectrales, Thèse de 3e cycle, Bordeaux (in preparation).

    Google Scholar 

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

    MATH  Google Scholar 

  13. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, Berlin, 1973.

    Book  MATH  Google Scholar 

  14. _____, Numerical Ranges II, London Math. Soc. Lecture Note Series 10, Cambridge University Press, 1973.

    Google Scholar 

  15. S. Brown, B. Chevreau and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory, 1 (1979), 123–126.

    MathSciNet  MATH  Google Scholar 

  16. L. Carleson, Interpolation by bounded analytic functions and the corona problem, Annals of Math., 76 (1962), 547–559.

    Article  MathSciNet  MATH  Google Scholar 

  17. I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New-York, 1968.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc., 10 (1978), 129–183.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. G. Dales, Convlution algebras on the real line, this Volume.

    Google Scholar 

  21. A. M. Davie, Invariant subspaces for Bishop's operators, Bull. Lond. Math. Soc., 6 (1974), 343–348.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  23. P. Enflo, On the Invariant Subspace Problem in Banach Spaces, Mittag-Leffler Institute Publications.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  25. _____, Elements for a classification of commutative radical Banach algebras, this Volume.

    Google Scholar 

  26. W. Feller, On the generation of unbounded semigroups of bounded linear operators, Annals of Math., (2) 58 (1953), 166–174.

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Fisher, The convex hull of finite Blaschke products, Bull. Amer. Math. Soc., 74 (1968), 1128–1129.

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Foias and W. Mlak, The extended spectrum of completely nonunitary contractions and the spectral mapping theorem, Studia Math., 26 (1966), 239–245.

    MathSciNet  MATH  Google Scholar 

  29. B. Sz-Nagy and C. Foias, Analyse Harmonique des Operateurs de L'espace de Hilbert, Akademiai Kiadó, Budapest, 1967.

    MATH  Google Scholar 

  30. C. Foias, C. M. Pearcy and B. Sz-Nagy, Contractions with spectral radius one and invariant subspaces, Acta Sci. Math., 43 (1981), 273–280.

    MathSciNet  MATH  Google Scholar 

  31. E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloquium Publications 31, Providence, 1957.

    Google Scholar 

  32. H. Hogbe-Nlend, Theorie des Bornologies et Applications, Springer-Verlag Lecture Notes, 273, 1971.

    Google Scholar 

  33. _____, Les fondements de la theorie spectrale des algèbres bornologiques, Bol. Soc. Brasil Math., 3 (1972).

    Google Scholar 

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

    Article  MATH  Google Scholar 

  35. Ju Kwei Wang, Multipliers of commutative Banach algebras, Pacific J. Math., 11 (1961), 1131–1149.

    Article  MathSciNet  MATH  Google Scholar 

  36. P. Koosis, Introduction to Hp Spaces, London Math Soc. Lecture Note Series 40, Cambridge University Press, 1980.

    Google Scholar 

  37. K. Koua, Multiplicateurs et quasimultiplicateurs dans les algèbres de Banach commutatives non-unitaires à unité approchée bornée, Thèse de 3e cycle, Bordeaux, Juin 1982.

    Google Scholar 

  38. _____, Un exemple d'algèbre de Banach commutative et radicale à unité approchée bornee sans multiplicateur non-trivial, submitted.

    Google Scholar 

  39. V. J. Lomonosov, Invariant subspaces for operators commuting with a compact operator, Funk. Anal. i Prilozen,7 (1973), 55–56.

    MathSciNet  Google Scholar 

  40. B. Nyman, On the one dimensional translation group on certain function spaces, Thesis, Uppsala, 1960.

    Google Scholar 

  41. H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer-Verlag, New York, 1973.

    Book  MATH  Google Scholar 

  42. M. Raouyane, Image numerique et elements hermitiens dans les algèbres bornologiques multiplicativement convexes complètes, Thèse de 3e cycle, Bordeaux, Décembre 1981.

    Google Scholar 

  43. M. Rome, Dilatations isometriques d'operateurs et le problème des sous espaces invariants, J. Operator Theory, 6 (1981), 39–50.

    MathSciNet  MATH  Google Scholar 

  44. I. Segal, Nine Introductions in Complex Analysis, Notas de Matematica 80, North Holland Math. Studies, North Holland, Amsterdam, 1981.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  46. _____, Cohen's factorization methods using an algebra of analytic functions, Proc. London Math. Soc., 39 (1979), 451–468.

    Article  MathSciNet  MATH  Google Scholar 

  47. _____, Continuous Semigroups in Banach Algebras, London Math. Soc. Lecture Note Series 63, Cambridge University Press, 1982.

    Google Scholar 

  48. N. Th. Varopoulos, Continuité des formes lineaires positives sur une algèbre de Banach avec involution, C. R. Acad. Sci. Paris Serie A–B, 258 (1964), 1121–1124.

    MathSciNet  MATH  Google Scholar 

  49. J. Wermer, The existence of invariant subspaces, Duke Math. J., 19 (1952), 615–622.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  51. ____, Semigroupes reels 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

John M. Bachar William G. Bade Philip C. Curtis H. Garth Dales Marc P. Thomas

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Esterle, J. (1983). Quasimultipliers, representations of H, and the closed ideal problem for commutative 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/BFb0064548

Download citation

  • DOI: https://doi.org/10.1007/BFb0064548

  • 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

Publish with us

Policies and ethics