Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy
Bulletin de la Société Mathématique de France, Volume 103 (1975), p. 441-509
@article{BSMF_1975__103__441_0,
     author = {Dineen, Se\'an},
     title = {Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {103},
     year = {1975},
     pages = {441-509},
     doi = {10.24033/bsmf.1811},
     zbl = {0328.46045},
     mrnumber = {54 \#11058},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_1975__103__441_0}
}
Dineen, Seán. Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy. Bulletin de la Société Mathématique de France, Volume 103 (1975) pp. 441-509. doi : 10.24033/bsmf.1811. http://www.numdam.org/item/BSMF_1975__103__441_0/

[1] Bochnak (J.) and Siciak (J.). - Analytic functions in Banach spaces, Studia Math., t. 35, 1970, p. 273-292. | MR 42 #8275 | Zbl 0199.18402

[2] Bogdanowitz (W. M.). - Analytic continuation of holomorphic functions with values in a locally convex space, Proc. Amer. math. Soc., t. 22, 1969, p. 660-666. | MR 40 #3308 | Zbl 0182.19201

[3] Cathelineau (J. L.). - Sur les modules topologiques, J. Math pures et appl., t. 47, 1969, p. 13-57. | MR 39 #6040 | Zbl 0174.16904

[4] Coeuré (G.). - Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'étude des fonctions analytiques, Ann. Inst. Fourier, Grenoble, t. 23, 1970, fasc. 1. p. 361-432. | Numdam | Zbl 0187.39003

[5] Colombeau (J. F.). - Quelques exemples singuliers d'applications G-analytiques, analytiques et différentiables en dimension infinie, C. R. Acad. Sc. Paris, t. 273, 1971, Série A, p. 158-160. | MR 44 #765 | Zbl 0221.46035

[6] Colombeau (J. F.). - Sur les applications G-analytiques et analytiques en dimension infinie, " Séminaire P. Lelong, 1971/1972 ", p. 48-58. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 332). | MR 52 #6418 | Zbl 0262.46048

[7] Dineen (S.). - Runge's theorem for Banach spaces, Proc. Roy. Irish. Acad., t. 71 (a), 1971, p. 85-89. | MR 46 #9392 | Zbl 0212.14801

[8] Dineen (S.). - Unbounded holomorphic functions on a Banach space, J. Lond. math. Soc., t. 4, 1972, p. 461-465. | MR 45 #5753 | Zbl 0244.46015

[9] Dineen (S.). - Fonctions analytiques dans les espaces vectoriels topologiques localement convexes, C. R. Acad. Sc. Paris, t. 274, 1972, Série A, p. 544-574. | MR 45 #877 | Zbl 0229.46024

[10] Dineen (S.). - Holomorphically complete locally convex topological vector spaces, « Séminaire P. Lelong, 1971/1972 », p. 77-111. - Berlin, Springer-Verlag, 1973, (Lecture Notes in Mathematics, 332). | MR 51 #13684 | Zbl 0278.46005

[11] Dineen (S.). - Holomorphically significant properties of topological vector spaces, "Colloque sur les fonctions analytiques de plusieurs variables complexes, Paris, 1972" (to appear in Agora Mathematica, Gauthier-Villars, Paris).

[12] Dineen (S.). - Holomorphic functions on locally convex topological vector spaces, I : Locally convex topologies on ℋ(U), Ann. Inst. Fourier, Grenoble, t. 23, 1973, fasc. 1, p. 19-54. | Numdam | MR 58 #17843 | Zbl 0241.46022

[13] Dineen (S.). - Holomorphic functions on locally convex topological vector spaces, II : Pseudo-convex domains, Ann. Inst. Fourier, Grenoble, t. 23, 1973, fasc. 3, p. 155-185. | Numdam | MR 58 #22652 | Zbl 0266.46019

[14] Dineen (S.). - Holomorphic functions and surjective limits, " Proceedings on infinite dimensional holomorphy ", p. 1-12. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 364). | MR 54 #11057 | Zbl 0277.46006

[15] Grothendieck (A.). - Sur les espaces (F) et (DF), Summa Brasil. Math., t. 3, 1954, p. 57-123. | MR 17,765b | Zbl 0058.09803

[16] Hirschowitz (A.). - Remarques sur les ouverts d'holomorphie d'un produit dénombrable de droites, Ann. Inst. Fourier, Grenoble, t. 22, 1972, p. 255-292. | Numdam | MR 49 #11256

[17] Hirschowitz (A.). - Prolongement analytiques en dimension infinie, Ann. Inst. Fourier, Grenoble, t. 22, 1972, p. 255-292. | Numdam | MR 49 #11256 | Zbl 0224.32015

[18] Hirschowitz (A.). - Sur un théorème de M. A. Zorn, Archiv der Mathematik, t. 23, 1972, p. 77-79. | MR 46 #6025 | Zbl 0239.46037

[19] Hirschowitz (A.). - Convexité abstraite et espaces normés, " Séminaire P. Lelong, 1970/1971 ", p. 1-13. - Berlin, Springer-Verlag, 1972 (Lecture Notes in Mathematics, 275). | MR 52 #6420 | Zbl 0257.46109

[20] Hogbe-Nlend (H.). - Théorie des bornologies et applications. - Berlin, Springer-Verlag, 1970 (Lecture Notes in Mathematics, 213). | Zbl 0225.46005

[21] Hogbe-Nlend (H.). - Sur la métrisabilité des espaces de fonctions holomorphes en dimension infinie, Bull. Sc. Math, Série 2, t. 97, 1973, p. 29-32. | MR 48 #6931 | Zbl 0271.46017

[22] Horvath (J.). - Topological vector spaces and distributions, Vol. I. - Reading, Addison - Wesley publishing Company, 1966 (Addison-Wesley Series in Mathematics). | MR 34 #4863 | Zbl 0143.15101

[23] Horvath (J.). - Finite parts of distributions, "Proceedings of the conference on linear operators and approximation", p. 142-158. - Basel, Birkhauser Verlag, 1972 (International Series of numerical Mathematics, 20). | MR 52 #6409 | Zbl 0253.46091

[24] Husain (T.). - Two new classes of locally convex spaces, Math. Ann., t. 166, 1966, p. 289-299. | MR 35 #3406 | Zbl 0143.34903

[25] Josefson (B.). - A counterexample to the Levi-problem, " Proceedings on infinite dimensional holomorphy ", p. 168-177. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 364). | MR 52 #14384 | Zbl 0285.32017

[26] Koethe (G.). - Topological vector spaces. - Berlin, Springer-Verlag, 1971. | Zbl 0417.46001

[27] Lazet (D.). - Applications analytiques dans les espaces bornologiques, " Séminaire P. Lelong, 1971/1972 ", p. 1-47. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 332). | MR 55 #1376 | Zbl 0262.46047

[28] Ligocka (E.). - A local factorization of analytic functions and its applications, Studia Math., t. 68, 1973, p. 239-252. | MR 50 #994 | Zbl 0261.46006

[29] Ligocka (E.) and Siciak (J.). - Weak analytic continuation, Bull. Acad. pol. Sc., t. 20, 1972, p. 461-466. | MR 47 #5896 | Zbl 0241.46013

[30] Nachbin (L.). - Topology on spaces of holomorphic mappings. - Berlin, Springer-Verlag, 1969 (Ergebnisse der Mathematik, 47). | MR 40 #7787 | Zbl 0172.39902

[31] Nachbin (L.). - Sur les espaces vectoriels topologiques d'applications continues, C. R. Acad. Sc. Paris, t. 271, 1970, Série A, p. 596-598. | MR 42 #6593 | Zbl 0205.12402

[32] Nachbin (L.). - Uniformité holomorphe et type exponentiel, " Séminaire P. Lelong, 1970/1971 ", p. 216-224. - Berlin, Springer-Verlag, 1971 (Lecture Notes in Mathematics, 205). | Zbl 0218.46024

[33] Nachbin (L.). - On vector valued versus scalar holomorphic continuation, Indag. Math., t. 35, 1973, fasc. 4, p. 352-354. | MR 48 #9395 | Zbl 0271.46018

[34] Noverraz (Ph.). - Fonctions plurisous harmoniques et analytiques dans les espaces vectorials topologiques complexes, Ann. Inst. Fourier, Grenoble, t. 19, 1969, p. 419-493. | Numdam | Zbl 0176.09903

[35] Noverraz (Ph.). - Pseudo-convexité, convexité polynomiale et domaines d'holomorphie en dimension infinie. - Amsterdam, North-Holland publishing Company, 1973 (Notas de Matematica, 48 ; North-Holland Mathematics Studies, 3). | Zbl 0251.46049

[36] Pietsch (A.). - Nuclear locally convex spaces. - Berlin, Springer-Verlag, 1972 (Ergebnisse der Mathematic, 66). | MR 50 #2853 | Zbl 0236.46001

[37] Pisanelli (D.). - Applications analytiques en dimension infinie, Bull. Sc. math., Série 2, t. 96, 1972, p. 181-191. | MR 45 #3788 | Zbl 0241.46042

[38] Rickart (C. E.). - Analytic functions of an infinite number of complex variables, Duke Math. J., t. 36, 1969, p. 581-597. | MR 40 #7819 | Zbl 0181.14304

[39] Schottenloher (M.). - Analytische Fortsetzung in Banachraumen, Math. Ann., t. 199, 1972, p. 313-336. | MR 50 #2566 | Zbl 0241.46014

[40] Schottenloher (M.). - ε-product and continuation of analytic mappings, " Colloque d'Analyse, Rio de Janeiro, 1972 ". - Paris, Hermann (to appear). | Zbl 0308.46044

[41] Schottenloher (M.). - The envelope of holomorphy as a functor, " Colloque sur les fonctions analytiques de plusieurs variables complexes, Paris, 1972 " (to appear in Agora Mathematica, Gauthier-Villars). | Zbl 0309.46043

[42] Tarzioglu (T.). - On Schwartz spaces, Math. Ann., t. 182, 1969, p. 236-242. | MR 40 #683 | Zbl 0179.45501

[43] Warner (S.). - Compact convergence on function spaces, Duke Math. J., t. 25, 1958, p. 265-282. | MR 21 #1521 | Zbl 0081.32802

[44] Zorn (M. A.). - Gateaux differentiability and essential boundedness, Duke Math. J., t. 12, 1945, p. 579-583. | MR 7,308a | Zbl 0061.25001