Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras

J. Esterle

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 5, page 539-582
  • ISSN: 0012-9593

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Esterle, J.. "Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras." Annales scientifiques de l'École Normale Supérieure 29.5 (1996): 539-582. <http://eudml.org/doc/82417>.

@article{Esterle1996,
author = {Esterle, J.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {character on a Fréchet algebra necessarily continuous; continuum hypothesis},
language = {eng},
number = {5},
pages = {539-582},
publisher = {Elsevier},
title = {Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras},
url = {http://eudml.org/doc/82417},
volume = {29},
year = {1996},
}

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
PB - Elsevier
VL - 29
IS - 5
SP - 539
EP - 582
LA - eng
KW - character on a Fréchet algebra necessarily continuous; continuum hypothesis
UR - http://eudml.org/doc/82417
ER -

References

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  1. [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). Zbl0243.46059MR46 #4201
  2. [2] R. ARENS, Dense inverse limit rings (Michigan Math. J., Vol. 5, 1958, pp. 169-182). Zbl0087.31802MR21 #3780
  3. [3] R. ARENS, The analytic functional calculus in commutative topological algebras (Pac. J. Math., Vol. 11, 1961, pp. 405-429). Zbl0109.34203MR25 #4373
  4. [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). Zbl0144.17003MR33 #3126
  5. [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). Zbl0007.21502JFM59.0344.02
  6. [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). Zbl52.0373.04JFM52.0373.04
  7. [7] E. BOREL, Sur les zéros des fonctions entières (Acta Math., Vol. 20, 1897, pp. 357-396). Zbl28.0360.01JFM28.0360.01
  8. [8] N. BOURBAKI, Topologie Générale, Chap. II, Hermann, Paris, 1960. 
  9. [9] D. CLAYTON, A reduction of the continuous homomorphism problem for F-algebras (Rocky Mountain J. Math., Vol. 5, 1975, pp. 337-344). Zbl0325.46055MR52 #11594
  10. [10] D. COUTY, Formes réduites des automorphismes de ℂn à variété linéaire fixe et répulsive (Springer Lect. Notes, Vol. 1404, 1989, pp. 346-410). Zbl0712.32007MR91c:32022
  11. [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). Zbl0219.46035MR44 #4524
  12. [12] H. G. DALES, A discontinuous homomorphism from C(X) (Amer. J. Math., (1), Vol. 101, 1979, pp. 647-734). Zbl0417.46054MR81g:46066
  13. [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). Zbl0365.46042MR57 #13498b
  14. [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). Zbl0629.03030MR90d:03101
  15. [15] A. M. DAVIE, Homotopy in Fréchet algebras (Proc. London Math. Soc., (3), Vol. 23, 1971, pp. 31-52). Zbl0218.46044MR45 #5756
  16. [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). Zbl0608.32008MR88d:46090
  17. [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). Zbl0411.46037MR58 #2298
  18. [18] J. ESTERLE, Sur l'existence d'un homomorphisme discontinu de C(K) (Proc. London Math. Soc., (3), Vol. 36, 1978, pp. 46-58). Zbl0411.46038MR58 #2299
  19. [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). Zbl0411.46039MR58 #2300
  20. [20] J. ESTERLE, Homomorphismes discontinus des algèbres de Banach commutatives séparables (Studia Math., Vol. 66, 1979, pp. 119-141). Zbl0353.46045MR81m:46067
  21. [21] J. ESTERLE, Universal properties of some commutative radical Banach algebras (J. Reine Ang. Math., Vol. 321, 1981, pp. 1-24). Zbl0438.46037MR82i:46078
  22. [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). Zbl0569.46031MR86a:46056
  23. [23] J. ESTERLE, Real semigroups in commutative Banach algebras (Springer Lect. Notes, Vol. 1221, 1986, pp. 16-35). Zbl0626.46048MR88c:46061
  24. [24] J. ESTERLE, Idéaux maximaux denses dans les algèbres de Fréchet (Bull. Sci. Math., Vol. 119, 1995, pp. 187-194). Zbl0826.46043MR96d:46070
  25. [25] J. ESTERLE, Propriétés multiplicatives universelles de certains quotients d'algèbres de Fréchet, submitted. 
  26. [26] P. FATOU, Sur certaines fonctions uniformes de deux variables (C. R. Acad. Sci. Paris, Vol. 175, 1922, pp. 1030-1033). Zbl48.0391.03JFM48.0391.03
  27. [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). Zbl0761.32015MR93d:32040
  28. [28] R. FRANKIEWICZ and P. ZBIERSKI, Hausdorff gaps and limits, Van Nostrand, 1994. Zbl0821.54001MR96d:03002
  29. [29] L. FUCHS, Partially ordered algebraic systems, Pergamon Press, Oxford, 1963. Zbl0137.02001MR30 #2090
  30. [30] L. GRUMANN, L'image d'une application holomorphe (Annales Fac. Sci. Toulouse, (1), 12, 1991, pp. 75-101). Zbl0749.32016MR94a:32039
  31. [31] R. C. GUNNING and H. ROSSI, Analytic functions of several complex variables, Prentice Hall, Englewood Cliffs, 1965. Zbl0141.08601MR31 #4927
  32. [32] H. HAHN, Über die nichtarchimedischen Gröβensysteme (S. B. Akad. Wiss. Wien, Vol. 116, 1907, pp. 601-655). Zbl38.0501.01JFM38.0501.01
  33. [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. [34] J. H. HUBBARD and R. OBERSTE-VORTH, Henon mappings in the complex domain (preprint). Zbl0839.54029
  35. [35] S. MacLANE, The universality of power series fields (Bull. Amer. Math. Soc., Vol. 45, 1939, pp. 888-890). Zbl0022.30401MR1,102cJFM65.0093.02
  36. [36] E. A. MICHAEL, Locally multiplicatively convex topological algebras (Mem. Amer. Math. Soc., Vol. 11, 1952). Zbl0047.35502MR14,482a
  37. [37] J. MUJICA, Complex analysis in Banach spaces. Holomorphic functions and domains of holomorphy in infinite dimensions, North Holland, 1986. Zbl0586.46040
  38. [38] R. NEVANLINNA, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929. JFM55.0773.03
  39. [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). Zbl0574.32036MR86h:32043
  40. [40] Y. NISHIMURA, Applications holomorphes injectives à jacobien constant de deux variables (J. Math. Kyoto Univ., (4), Vol. 26, 1986, pp. 697-709). Zbl0625.32022MR87m:32054
  41. [41] E. PICARD, Sur les fonctions entières (C. R. Acad. Sci. Paris, Vol. 89, 1879, pp. 662-665). JFM11.0268.01
  42. [42] H. POINCARÉ, Sur une classe nouvelle de transcendantes uniformes (J. de Mathématiques, Vol. 6, 1890, pp. 313-355). JFM22.0420.01
  43. [43] J. P. ROSAY and W. RUDIN, Holomorphic maps from ℂn to ℂn (Trans. Amer. Math. Soc., (1), Vol. 310, 1988, pp. 47-86). Zbl0708.58003MR89d:32058
  44. [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). Zbl0780.32002MR93k:32045
  45. [45] H. ROYDEN, Function algebras (Bull. Amer. Math. Soc., Vol. 69, 1963, pp. 281-298). Zbl0111.11802MR26 #6817
  46. [46] M. SCHOTTENLOHER, Michael problem and algebras of holomorphic functions (Arch. Math., Vol. 37, 1981, pp. 241-247). Zbl0471.46036MR83b:46061
  47. [47] T. S. SHAH, On semi-normed rings with involution (Izv. Akad. Nauk. SSSR, (Russian), Vol. 23, 1959, pp. 509-528). MR22 #4968
  48. [48] A. M. SINCLAIR, Continuous semigroups in Banach algebras (London Math. Soc. Lect. Notes, Vol. 63, 1982). Zbl0493.46042MR84b:46053
  49. [49] M. THOMAS, The image of a derivation is contained in the radical (Ann. of Math., Vol. 128, 1988, pp. 435-460). Zbl0681.47016MR90d:46075
  50. [50] W. H. WOODIN, Set theory and discontinuous homomorphisms from Banach algebras (Ph. D. Thesis, University of California at Berkeley, 1984). 
  51. [51] W. H. WOODIN, A discontinuous homomorphism from C(X) without CH (J. London Math. Soc., (2), Vol. 48, 1993, pp. 299-315). Zbl0804.46063MR94g:46055
  52. [52] O. ZARISKI and P. SAMUEL, Commutative Algebra, Vol. II, Van Nostrand, 1960. Zbl0121.27801MR22 #11006
  53. [53] W. ZELASKO, Maximal ideals in commutative m-convex algebras (Studia Math., Vol. 58, 1976, pp. 291-298). Zbl0344.46103MR55 #8803
  54. [54] F. ZOUAKIA, The theory of Cohen elements (Springer Lect. Notes, Vol. 975, 1983, pp. 163-178). Zbl0504.46037MR84f:46069
  55. [55] F. ZOUAKIA, Semigroupes réels dans les algèbres de Banach commutatives (J. London Math. Soc., (2), Vol. 35, 1987, pp. 543-552). Zbl0651.46054MR89c:46067

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