The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition

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1. [1] V. AURICH, The spectrum as envelope of holomorphy of a domain over an arbitrary product of complex lines. In : Proceedings on Infinite Dimensional Holomorphy (Lexington 1973), pp. 109-122. Springer Lecture Notes, 364 (1974). Zbl0278.32019
2. [2] G. GOEURÉ, Analytic functions and manifolds in infinite dimensional spaces. Amsterdam : North-Holland 1974. Zbl0282.32015
3. [3] S. DINEEN, Holomorphic functions on locally convex topological vector spaces II. Pseudoconvex domains, Ann. Inst. Fourier, 23 (1973), 155-185. Zbl0266.46019MR58 #22652
4. [4] S. DINEEN, Surieties and holomorphic functions in infinite dimensions. Bull. Soc. math. France, 103 (1975), 441-509. Zbl0328.46045
5. [5] S. DINEEN et Ph. NOVERRAZ, Le problème de Levi dans certains espaces vectoriels topologiques localement convexes, C.R. Acad. Sci., Paris, 278, A (1974), 693-695. And in full length with Schottenloher, M. : Bull. Soc. math. France, 104 (1976), 87-97. Zbl0334.46049
6. [6] K. FLORET and J. WLOKA, Einführung in die Theorie der lokalkonvexen Räume, Springer Lecture Notes, 56 (1968). Zbl0155.45101MR37 #1945
7. [7] T. FIGIEL and W. B. JOHNSON, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc., 41 (1973), 197-200. Zbl0289.46015MR49 #5782
8. [8] L. GRUMAN, The Levi problem in certain infinite dimensional vector spaces, Ill. J. Math., 18 (1974), 20-26. Zbl0276.32017MR50 #993
9. [9] L. GRUMAN et C. O. KISELMAN, Le problème de Levi dans les espaces de Banach à base, C.R. Acad. Sci., Paris, 274, A (1972), 1296-1299. Zbl0243.32017MR45 #3759
10. [10] Y. HERVIER, Sur le problème de Levi pour les espaces étalés banachiques, C.R. Acad. Sci., 275, A (1972), 821-824. Zbl0243.32018MR47 #2098
11. [11] A. HIRSCHOWITZ, Prolongement analytique en dimension infinie, Ann. Inst. Fourier, 22 (1972), 255-292. Zbl0224.32015MR49 #11256
12. [12] L. HÖRMANDER, An introduction to complex analysis in several variables, Princeton, Van Nostrand 1966. Zbl0138.06203
13. [13] B. JOSEFSON, A counterexample to the Levi problem. In : Proceedings on Infinite Dimensional Holomorphy (Lexington 1973), pp. 168-177. Springer Lecture Notes, 364 (1974). Zbl0285.32017
14. [14] B. JOSEFSON, Weak sequential convergence in the dual of a Banach space does not imply norm convergence. Arkiv för Mat., 13 (1975), 79-89. Zbl0303.46018MR51 #11067
15. [15] E. LIGOCKA, A local factorization of analytic functions and its applications, Studia Math., 47 (1973), 239-252. Zbl0261.46006MR50 #994
16. [16] J. T. MARTI, Introduction to the theory of bases, Springer Tracts in Natural Philosophy, 18 (1969). Zbl0191.41301MR55 #10994
17. [17] M. C. MATOS, Domains of τ-holomorphy in a separable Banach space, Math. Ann., 195 (1972), 273-278. Zbl0215.48302MR45 #2472
18. [18] L. NACHBIN, Uniformité holomorphe et type exponentiel. In : Sém. P. Lelong, 1970/1971, pp. 216-224. Springer Lecture Notes, 205 (1971). Zbl0218.46024
19. [19] Ph. NOVERRAZ, Pseudo-convexité, convexité polynomiale et domaines d'holomorphie en dimension infinie, Amsterdam, North-Holland, 1973. Zbl0251.46049
20. [20] Ph. NOVERRAZ, Approximation of holomorphic or plurisubharmonic functions in certain Banach spaces. In : Proceedings on Infinite Dimensional Holomorphy (Lexington 1973), pp. 178-185. Springer Lecture Notes, 364 (1974). Zbl0284.46018
21. [21] Ph. NOVERRAZ, Le problème de Levi dans certains espaces de Silva. Preprint. 
22. [22] K. OKA, Domaines finis sans point critique intérieur, Jap. J. Math., 27 (1953), 97-155. Zbl0053.24302MR17,82b
23. [23] A. PELCZYNSKI and P. WOJTASZCYK, Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces, Studia Math., 40 (1971), 91-108. Zbl0221.46014MR47 #2319
24. [24] R. POMÈS, Solution du problème de Levi dans les espaces de Silva à base, C.R. Acad. Sci., Paris, 278, A (1974), 707-710. Zbl0278.32021MR49 #11257
25. [25] N. POPA, Sur le problème de Levi dans les espaces de Silva à base, C.R. Acad. Sci., Paris, 277, A (1973), 211-214. Zbl0261.32006MR51 #8464
26. [26] M. SCHOTTENLOHER, Über analytische Fortsetzung in Banachräumen, Math. Ann., 199 (1972), 313-336. Zbl0241.46014MR50 #2566
27. [27] M. SCHOTTENLOHER, The envelope of holomorphy as a functor. In : Fonctions analytiques de plusieurs variables et analyse complexe (Coll. Intern. du C.N.R.S., Paris 1972), pp. 221-230. Paris : Gauthier-Villars 1974. Zbl0309.46043
28. [28] M. SCHOTTENLOHER, Bounding sets in Banach spaces and regular classes of analytic functions. In : Functional Analysis and Applications (Recife 1972), pp. 109-122. Springer Lecture Notes, 384 (1974). Zbl0285.46014
29. [29] M. SCHOTTENLOHER, Riemann domains. Basic results and open questions. In : Proceedings on Infinite Dimensional Holomorphy (Lexington 1973), pp. 196-212. Springer Lecture Notes, 364 (1974). Zbl0281.32022
30. [30] M. SCHOTTENLOHER, Analytic continuation and regular classes in locally convex Hausdorff spaces, Port. Math., 33 (1974), 219-250. Zbl0293.32023MR50 #8071
31. [31] M. SCHOTTENLOHER, Das Leviproblem in unendlichdimensionalen Räumen mit Schauderzerlegung. Habilitationsschrift, München 1974. 

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