Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 5, pp. 539-582.
@article{ASENS_1996_4_29_5_539_0,
     author = {Esterle, J.},
     title = {Picard's theorem, {Mittag-Leffler} methods, and continuity of characters on {Fr\'echet} algebras},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {539--582},
     publisher = {Elsevier},
     volume = {Ser. 4, 29},
     number = {5},
     year = {1996},
     doi = {10.24033/asens.1748},
     mrnumber = {98f:46043},
     zbl = {0890.46039},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1748/}
}
TY  - JOUR
AU  - Esterle, J.
TI  - Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1996
SP  - 539
EP  - 582
VL  - 29
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1748/
DO  - 10.24033/asens.1748
LA  - en
ID  - ASENS_1996_4_29_5_539_0
ER  - 
%0 Journal Article
%A Esterle, J.
%T Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
%J Annales scientifiques de l'École Normale Supérieure
%D 1996
%P 539-582
%V 29
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.24033/asens.1748/
%R 10.24033/asens.1748
%G en
%F ASENS_1996_4_29_5_539_0
Esterle, J. Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 29 (1996) no. 5, pp. 539-582. doi : 10.24033/asens.1748. http://www.numdam.org/articles/10.24033/asens.1748/

[1] G. R. Allan, Embedding the algebra of all formal power series in a Banach algebra (Proc. London Math. Soc. (3), Vol. 25, 1972, pp. 329-340). | MR | Zbl

[2] R. Arens, Dense inverse limit rings (Michigan Math. J., Vol. 5, 1958, pp. 169-182). | MR | Zbl

[3] R. Arens, The analytic functional calculus in commutative topological algebras (Pac. J. Math., Vol. 11, 1961, pp. 405-429). | MR | Zbl

[4] R. Arens, To what extent does the space of maximal ideals determine the algebras (Function Algebras Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965, Scott-Foresman, Chicago, Illinois, 1966, pp. 164-168). | MR | Zbl

[5] L. Bieberbach, Beispiel zweier ganzer Funktionen zweier komplexer Variablen, welche eine schlichte volumtreue Abbildung des ℝ4 auf einen Teil seiner selbst vermitteln (S. B. Preuss Akad. Wiss., Vol. 14/15, 1933, pp. 476-479). | JFM | Zbl

[6] A. Bloch, Sur les systèmes de fonctions uniformes satisfaisant à l'équation d'une variété algébrique dont l'irrégularité dépasse la dimension (J. Math. Pures et Appl., (1), Vol. 5, 1926, pp. 19-66). | JFM | Numdam

[7] E. Borel, Sur les zéros des fonctions entières (Acta Math., Vol. 20, 1897, pp. 357-396). | JFM

[8] N. Bourbaki, Topologie Générale, Chap. II, Hermann, Paris, 1960.

[9] D. Clayton, A reduction of the continuous homomorphism problem for F-algebras (Rocky Mountain J. Math., Vol. 5, 1975, pp. 337-344). | MR | Zbl

[10] D. Couty, Formes réduites des automorphismes de ℂn à variété linéaire fixe et répulsive (Springer Lect. Notes, Vol. 1404, 1989, pp. 346-410). | MR | Zbl

[11] I. Craw, A condition equivalent to the continuity of characters on a Fréchet algebra (Proc. London Math. Soc., (3), Vol. 22, 1971, pp. 452-464). | MR | Zbl

[12] H. G. Dales, A discontinuous homomorphism from C(X) (Amer. J. Math., (1), Vol. 101, 1979, pp. 647-734). | MR | Zbl

[13] H. G. Dales and J. P. Mcclure, Higher point derivations on commutative Banach algebras, II (J. London Math. Soc., (2), Vol. 16, 1977, pp. 313-325). | MR | Zbl

[14] H. G. Dales and W. H. Woodin, An introduction to independence for analysts (London Math. Soc. Lect. Notes, Vol. 115, Cambridge University Press, 1987). | MR | Zbl

[15] A. M. Davie, Homotopy in Fréchet algebras (Proc. London Math. Soc., (3), Vol. 23, 1971, pp. 31-52). | MR | Zbl

[16] P. G. Dixon and J. Esterle, Michael's problem and the Poincaré-Fatou-Bieberbach phenomenon (Bull. A.M.S., (2), Vol. 15, 1986, pp. 127-187). | MR | Zbl

[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, Vol. 30, 1977, pp. 113-127). | MR | Zbl

[18] J. Esterle, Sur l'existence d'un homomorphisme discontinu de C(K) (Proc. London Math. Soc., (3), Vol. 36, 1978, pp. 46-58). | MR | Zbl

[19] J. Esterle, Injection de semigroupes divisibles dans des algèbres de convolution et construction d'homomorphismes discontinus de C(K) (Proc. London Math. Soc., (3), Vol. 36, 1978, pp. 59-85). | MR | Zbl

[20] J. Esterle, Homomorphismes discontinus des algèbres de Banach commutatives séparables (Studia Math., Vol. 66, 1979, pp. 119-141). | MR | Zbl

[21] J. Esterle, Universal properties of some commutative radical Banach algebras (J. Reine Ang. Math., Vol. 321, 1981, pp. 1-24). | MR | Zbl

[22] J. Esterle, Mittag-Leffler methods in the theory of Banach algebras and a new approach to Michael's problem (Contemp. Math., Vol. 32, 1984, pp. 107-129). | MR | Zbl

[23] J. Esterle, Real semigroups in commutative Banach algebras (Springer Lect. Notes, Vol. 1221, 1986, pp. 16-35). | MR | Zbl

[24] J. Esterle, Idéaux maximaux denses dans les algèbres de Fréchet (Bull. Sci. Math., Vol. 119, 1995, pp. 187-194). | MR | Zbl

[25] J. Esterle, Propriétés multiplicatives universelles de certains quotients d'algèbres de Fréchet, submitted.

[26] P. Fatou, Sur certaines fonctions uniformes de deux variables (C. R. Acad. Sci. Paris, Vol. 175, 1922, pp. 1030-1033). | JFM

[27] J. E. Fornaess and N. Sibony, Complex Henon mappings in ℂ2 and Fatou-Bieberbach domains (Duke Math. J., (2), Vol. 65, 1992, pp. 345-380). | MR | Zbl

[28] R. Frankiewicz and P. Zbierski, Hausdorff gaps and limits, Van Nostrand, 1994. | MR | Zbl

[29] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford, 1963. | MR | Zbl

[30] L. Grumann, L'image d'une application holomorphe (Annales Fac. Sci. Toulouse, (1), 12, 1991, pp. 75-101). | Numdam | MR | Zbl

[31] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice Hall, Englewood Cliffs, 1965. | MR | Zbl

[32] H. Hahn, Über die nichtarchimedischen Gröβensysteme (S. B. Akad. Wiss. Wien, Vol. 116, 1907, pp. 601-655). | JFM

[33] G. H. Halphen, Sur la réduction des équations différentielles linéaires aux formes intégrables (Mémoires de l'Académie des Sciences, (1), Vol. 28, 1884, pp. 1-260).

[34] J. H. Hubbard and R. Oberste-Vorth, Henon mappings in the complex domain (preprint).

[35] S. Maclane, The universality of power series fields (Bull. Amer. Math. Soc., Vol. 45, 1939, pp. 888-890). | JFM | MR | Zbl

[36] E. A. Michael, Locally multiplicatively convex topological algebras (Mem. Amer. Math. Soc., Vol. 11, 1952). | MR | Zbl

[37] J. Mujica, Complex analysis in Banach spaces. Holomorphic functions and domains of holomorphy in infinite dimensions, North Holland, 1986. | Zbl

[38] R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929. | JFM

[39] Y. Nishimura, Applications holomorphes injectives de ℂ2 dans lui-même qui exceptent une droite complexe (J. Math. Kyoto. Univ., (4), Vol. 24, 1984, pp. 755-761). | MR | Zbl

[40] Y. Nishimura, Applications holomorphes injectives à jacobien constant de deux variables (J. Math. Kyoto Univ., (4), Vol. 26, 1986, pp. 697-709). | MR | Zbl

[41] E. Picard, Sur les fonctions entières (C. R. Acad. Sci. Paris, Vol. 89, 1879, pp. 662-665). | JFM

[42] H. Poincaré, Sur une classe nouvelle de transcendantes uniformes (J. de Mathématiques, Vol. 6, 1890, pp. 313-355). | JFM | Numdam

[43] J. P. Rosay and W. Rudin, Holomorphic maps from ℂn to ℂn (Trans. Amer. Math. Soc., (1), Vol. 310, 1988, pp. 47-86). | MR | Zbl

[44] J. P. Rosay and W. Rudin, Growth of volumes in Fatou-Bieberbach domains (Publ. Res. Inst. Math. Sci., Vol. 29, 1993, pp. 161-166). | MR | Zbl

[45] H. Royden, Function algebras (Bull. Amer. Math. Soc., Vol. 69, 1963, pp. 281-298). | MR | Zbl

[46] M. Schottenloher, Michael problem and algebras of holomorphic functions (Arch. Math., Vol. 37, 1981, pp. 241-247). | MR | Zbl

[47] T. S. Shah, On semi-normed rings with involution (Izv. Akad. Nauk. SSSR, (Russian), Vol. 23, 1959, pp. 509-528). | MR

[48] A. M. Sinclair, Continuous semigroups in Banach algebras (London Math. Soc. Lect. Notes, Vol. 63, 1982). | MR | Zbl

[49] M. Thomas, The image of a derivation is contained in the radical (Ann. of Math., Vol. 128, 1988, pp. 435-460). | MR | Zbl

[50] W. H. Woodin, Set theory and discontinuous homomorphisms from Banach algebras (Ph. D. Thesis, University of California at Berkeley, 1984).

[51] W. H. Woodin, A discontinuous homomorphism from C(X) without CH (J. London Math. Soc., (2), Vol. 48, 1993, pp. 299-315). | MR | Zbl

[52] O. Zariski and P. Samuel, Commutative Algebra, Vol. II, Van Nostrand, 1960. | MR | Zbl

[53] W. Zelasko, Maximal ideals in commutative m-convex algebras (Studia Math., Vol. 58, 1976, pp. 291-298). | MR | Zbl

[54] F. Zouakia, The theory of Cohen elements (Springer Lect. Notes, Vol. 975, 1983, pp. 163-178). | MR | Zbl

[55] F. Zouakia, Semigroupes réels dans les algèbres de Banach commutatives (J. London Math. Soc., (2), Vol. 35, 1987, pp. 543-552). | MR | Zbl

Cited by Sources: