Analytic sheaves in Banach spaces

Lempert, László; Patyi, Imre

doi:10.1016/j.ansens.2006.12.006

Lempert, László ; Patyi, Imre

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 453-486.

Zbl | 1 citation dans Numdam

DOI : 10.1016/j.ansens.2006.12.006

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     author = {Lempert, L\'aszl\'o and Patyi, Imre},
     title = {Analytic sheaves in {Banach} spaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {453--486},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {3},
     year = {2007},
     doi = {10.1016/j.ansens.2006.12.006},
     zbl = {1135.32008},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2006.12.006/}
}

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Lempert, László; Patyi, Imre. Analytic sheaves in Banach spaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 453-486. doi : 10.1016/j.ansens.2006.12.006. http://www.numdam.org/articles/10.1016/j.ansens.2006.12.006/

Bibliographie
Cité par

[1] Bishop E., Analytic functions with values in a Fréchet space, Pacific J. Math. 12 (1962) 1177-1192. | MR | Zbl

[2] Bredon G.E., Sheaf Theory, second ed., Springer, New York, 1997. | MR | Zbl

[3] Bungart L., Holomorphic functions with values in locally convex spaces and applications to integral formulas, Trans Amer. Math. Soc. 111 (1964) 317-344. | MR | Zbl

[4] Cartan H., Séminaire École Norm. Sup. 4, Fonctions analytiques de plusieurs variables complexes, Paris, 1951-52.

[5] Dineen S., Bounding subsets of a Banach space, Math. Ann. 192 (1971) 61-70. | MR | Zbl

[6] Docquier F., Grauert H., Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960) 94-123. | MR | Zbl

[7] Douady A., Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1966) 1-95. | Numdam | MR | Zbl

[8] Douady A., A remark on Banach analytic spaces, in: Symposium on Infinite-Dimensional Topology, Baton Rouge, LA, 1967, Ann. of Math. Studies, vol. 69, Princeton Univ. Press, Princeton, NJ, 1972, pp. 41-42. | MR | Zbl

[9] Griffiths P., Adams J., Topics in Algebraic and Analytic Geometry, Mathematical Notes, Princeton Univ. Press, Princeton, NJ, 1974. | MR | Zbl

[10] Josefson B., Bounding subsets of $l^{\infty} (A)$ , J. Math. Pures Appl. 57 (1978) 397-421. | MR | Zbl

[11] Josefson B., Approximations of holomorphic functions in certain Banach spaces, Internat. J. Math. 15 (2004) 467-471. | MR | Zbl

[12] Kelly G.M., Basic Concepts of Enriched Category Theory, Cambridge Univ. Press, Cambridge, 1982. | MR | Zbl

[13] Leiterer J., Banach coherent analytic Fréchet sheaves, Math. Nachr. 85 (1978) 91-109. | MR | Zbl

[14] Lempert L., The Dolbeault complex in infinite dimensions I, J. Amer. Math. Soc. 11 (1998) 485-520. | MR | Zbl

[15] Lempert L., Approximation de fonctions holomorphes d'un nombre infini de variables, Ann. Inst. Fourier (Grenoble) 49 (1999) 1293-1304. | Numdam | MR | Zbl

[16] Lempert L., Approximation of holomorphic functions of infinitely many variables II, Ann. Inst. Fourier (Grenoble) 50 (2000) 423-442. | Numdam | MR | Zbl

[17] Lempert L., The Dolbeault complex in infinite dimensions III, Invent. Math. 142 (2000) 579-603. | MR | Zbl

[18] Lempert L., Plurisubharmonic domination, J. Amer. Math. Soc. 17 (2004) 361-372. | MR | Zbl

[19] Lempert L., Vanishing cohomology for holomorphic vector bundles in a Banach setting, Asian J. Math. 8 (2004) 65-86. | MR | Zbl

[20] Meylan F., Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition, Ann. Scuola Norm. Sup. Pisa (2006). | Numdam | MR

[21] Mujica J., Complex Analysis in Banach Spaces, North-Holland, Amsterdam, 1986. | MR | Zbl

[22] Patyi I., On the $\bar{\partial}$ equation in a Banach space, Bull. Soc. Math. France 128 (2000) 391-406. | Numdam | MR | Zbl

[23] Patyi I., On the Oka principle in a Banach space, I, Math. Ann. 326 (2003) 417-441. | MR | Zbl

[24] Patyi I., On the Oka principle in a Banach space, II, Math. Ann. 326 (2003) 443-458. | MR | Zbl

[25] Patyi I., Cohomological characterization of pseudoconvexity in a Banach space, Math. Z. 245 (2003) 371-386. | MR | Zbl

[26] Patyi I., Analytic cohomology of complete intersections in a Banach space, Ann. Inst. Fourier (Grenoble) 54 (2004) 147-158. | Numdam | MR | Zbl

[27] Patyi I., On holomorphic Banach vector bundles over Banach spaces, manuscript, math.CV/0509557.

[28] Patyi I., An analytic Koszul complex in a Banach space, manuscript, math.CV/0509556.

[29] Patyi I., Analytic cohomology in a Banach space, manuscript, math.CV/0507520.

[30] Pestov V., Analytic subsets of Hilbert spaces, in: Fruchard A., Troesch A. (Eds.), Actes du colloque trajectorien, IRMA, Strasbourg, 1995, pp. 75-80. | MR

[31] Ramis J.P., Sous-ensembles analytiques d'une variété banachique complexe, Springer, Berlin-New York, 1970. | Zbl

[32] Serre J.-P., Faisceaux algébriques cohérents, Ann. Math. 61 (1955) 197-278. | MR | Zbl

[33] Singer I., Bases in Banach Spaces, I-II, Springer, Berlin, 1981. | Zbl

[34] Siu Y.T., Every Stein variety admits a Stein neighborhood, Invent. Math. 38 (1976/77) 89-100. | MR | Zbl

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