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References
M. Akkar, Etude spectrale et structure des algèbres topologiques et bornologiques complètes, Thèse de Doctorat d'Etat de Mathématiques, Bordeaux, 1976.
G. R. Allan, Elements of finite closed descent in a Banach algebra, J. London Math. Soc., 7 (1973), 462–466.
Ideals of rapidly growing functions, Proceedings International Symposium on functional analysis and its applications, Ibadan, Nigeria (1977), 85–109.
G. R. Allan, H. G. Dales and J. P. McClure, Pseudo-Banach algebras, Studia Math., 40 (1971), 55–69.
M. Altman, Contracteurs dans les algèbres de Banach, C. R. Acad. Sci. Paris Ser A-B, 274 (1972), 399–400.
C. Apostol, Functional calculus and invariant subspaces, J. Operator Theory, 4 (1980), 159–190.
A. Atzmon, Operators which are annihilated by analytic functions and invariant subspaces, Acta Math., 144 (1980), 27–63.
W. G. Bade and H. G. Dales, Norms and ideals in radical convolution algebras, J. Functional Analysis, 41 (1981), 77–109.
B. Beauzamy, Sous espaces invariants de type fonctionnel dans les espaces de Banach, Acta Math., 144 (1980), 65–82.
_____, Sous espaces invariants dans les espaces de Banach, Seminaire N. Bourbaki, 549, (Fevrier, 1980).
M. Berkani, Inegalités dans les algèbres de Banach et proprietés spectrales, Thèse de 3e cycle, Bordeaux (in preparation).
R. P. Boas, Entire Functions, Academic Press, New-York, 1954.
F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, Berlin, 1973.
_____, Numerical Ranges II, London Math. Soc. Lecture Note Series 10, Cambridge University Press, 1973.
S. Brown, B. Chevreau and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory, 1 (1979), 123–126.
L. Carleson, Interpolation by bounded analytic functions and the corona problem, Annals of Math., 76 (1962), 547–559.
I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New-York, 1968.
P. J. Cohen, Factorization in group algebras, Duke Math. J., 26 (1959), 199–206.
H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc., 10 (1978), 129–183.
H. G. Dales, Convlution algebras on the real line, this Volume.
A. M. Davie, Invariant subspaces for Bishop's operators, Bull. Lond. Math. Soc., 6 (1974), 343–348.
Y. Domar, A solution of the translation-invariant subspace problem for weighted LP on ℝ, ℝ+ or ℤ, this Volume.
P. Enflo, On the Invariant Subspace Problem in Banach Spaces, Mittag-Leffler Institute Publications.
J. Esterle, Universal properties of some commutative radical Banach algebras, J. für die Reine und ang. Math., 321 (1981), 1–24.
_____, Elements for a classification of commutative radical Banach algebras, this Volume.
W. Feller, On the generation of unbounded semigroups of bounded linear operators, Annals of Math., (2) 58 (1953), 166–174.
S. Fisher, The convex hull of finite Blaschke products, Bull. Amer. Math. Soc., 74 (1968), 1128–1129.
C. Foias and W. Mlak, The extended spectrum of completely nonunitary contractions and the spectral mapping theorem, Studia Math., 26 (1966), 239–245.
B. Sz-Nagy and C. Foias, Analyse Harmonique des Operateurs de L'espace de Hilbert, Akademiai Kiadó, Budapest, 1967.
C. Foias, C. M. Pearcy and B. Sz-Nagy, Contractions with spectral radius one and invariant subspaces, Acta Sci. Math., 43 (1981), 273–280.
E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloquium Publications 31, Providence, 1957.
H. Hogbe-Nlend, Theorie des Bornologies et Applications, Springer-Verlag Lecture Notes, 273, 1971.
_____, Les fondements de la theorie spectrale des algèbres bornologiques, Bol. Soc. Brasil Math., 3 (1972).
B. E. Johnson, Continuity of centralizers on Banach algebras, J. Lond Math. Soc., 41 (1966), 639–640.
Ju Kwei Wang, Multipliers of commutative Banach algebras, Pacific J. Math., 11 (1961), 1131–1149.
P. Koosis, Introduction to Hp Spaces, London Math Soc. Lecture Note Series 40, Cambridge University Press, 1980.
K. Koua, Multiplicateurs et quasimultiplicateurs dans les algèbres de Banach commutatives non-unitaires à unité approchée bornée, Thèse de 3e cycle, Bordeaux, Juin 1982.
_____, Un exemple d'algèbre de Banach commutative et radicale à unité approchée bornee sans multiplicateur non-trivial, submitted.
V. J. Lomonosov, Invariant subspaces for operators commuting with a compact operator, Funk. Anal. i Prilozen,7 (1973), 55–56.
B. Nyman, On the one dimensional translation group on certain function spaces, Thesis, Uppsala, 1960.
H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer-Verlag, New York, 1973.
M. Raouyane, Image numerique et elements hermitiens dans les algèbres bornologiques multiplicativement convexes complètes, Thèse de 3e cycle, Bordeaux, Décembre 1981.
M. Rome, Dilatations isometriques d'operateurs et le problème des sous espaces invariants, J. Operator Theory, 6 (1981), 39–50.
I. Segal, Nine Introductions in Complex Analysis, Notas de Matematica 80, North Holland Math. Studies, North Holland, Amsterdam, 1981.
A. M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Functional Analysis, 29 (1978), 308–318.
_____, Cohen's factorization methods using an algebra of analytic functions, Proc. London Math. Soc., 39 (1979), 451–468.
_____, Continuous Semigroups in Banach Algebras, London Math. Soc. Lecture Note Series 63, Cambridge University Press, 1982.
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.
J. Wermer, The existence of invariant subspaces, Duke Math. J., 19 (1952), 615–622.
F. Zouakia, The theory of Cohen elements, this Volume.
____, Semigroupes reels dans certaines algèbres de Banach commutatives radicales, Thèse de 3e cycle, Bordeaux, Juin, 1980.
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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
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