The Cartan-Thullen theorem for Banach spaces

Seán Dineen

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1970)

  • Volume: 24, Issue: 4, page 667-676
  • ISSN: 0391-173X

How to cite


Dineen, Seán. "The Cartan-Thullen theorem for Banach spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.4 (1970): 667-676. <>.

author = {Dineen, Seán},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {667-676},
publisher = {Scuola normale superiore},
title = {The Cartan-Thullen theorem for Banach spaces},
url = {},
volume = {24},
year = {1970},

AU - Dineen, Seán
TI - The Cartan-Thullen theorem for Banach spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1970
PB - Scuola normale superiore
VL - 24
IS - 4
SP - 667
EP - 676
LA - eng
UR -
ER -


  1. [1] Alexander, H., Analytic Functions on Banach spaces, Thesis, University of California at Berkeley, 1968. 
  2. [2] Bremermann, H.J., Holomorphic functionals and complex convexity in Banach spaces, Pacific J. of Math., 7 (1957), 811-831. Zbl0078.10901MR88709
  3. [3] Bremermann, H.J., Complex Convexity, Trans, Amer. Math. Soc., 82 (1956) 17-51. Zbl0070.30402MR79100
  4. [4] Cartan, II. and P. Thullen, Regularitäts — und Konvergenzbereiche, Math. Ann.106 (1932) 617-647. Zbl0004.35704MR1512777JFM58.0347.02
  5. [5] Chae, S.B., Holomorphic germs on Banach spaces, University of Rochester, Thesis (1969). 
  6. [6] Coeuré, G., Fonction plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'étude des fonction analytiques, Thesis, Université de Nancy (1969). 
  7. [7] Dineen, S., Holomorphy types on a Banach space, University of Maryland, Thesis, (1969) (to be published in Studia Math.). Zbl0235.32013MR304705
  8. [8] Dineen, S., Unbounded holomorphic functions on a Banach space, (to be published in Jour. Lond. Math. Soc.). Zbl0244.46015
  9. [9] Gupta, C.P., Malgrange theorem for nuclearly entire functions of bounded type on a Banach space, University of Rochester, Thesis (1966). Reproduced in Notas de Matematica Pura e Aplicada, Rio de Janeiro (1968). Zbl0182.45402MR632066
  10. [10] Gunning, R. and H. Rossi, Analytic functions of several complex variables, Prentice Hall, 1965. Zbl0141.08601MR180696
  11. [11] Hirschowitz, A., Remarques sur les ouverts d'holomorphie d'un produit dénombrable de droites., Annales de l'Institut Fourier, 19 (1969) 219-229. Zbl0207.08203MR252674
  12. [12] Hirschowitz, A., Sur le non-plongement des varietes analytiques banachiques Réelles. C. R. Acad. Sc., Paris, 269 (844-846) 1969. Zbl0205.12203MR253376
  13. [13] Hörmander, L., An introduction to complex analysis in several variables, Van Nostrand, 1966. Zbl0138.06203MR203075
  14. [14] Horváth, J., Topological vector spaces and distributions, Vol. I, Addison-Wesley, 1966. Zbl0143.15101MR205028
  15. [15] Nachbin, L., Holomorphic functions, domains of holomorphy and local properties. Lecture notes at the University of Rochester, 1967, Prepared by R. M. Aron. Zbl0208.10301MR274798
  16. [16] Nachbin, L., Thopology on spaces of holomorphic mappings. Ergebnisse der Matematik und ihre grenzgebiete 47. Springer-Verlag, Berlin (1969). Zbl0172.39902MR254579
  17. [17] Nachbin, L., Concerning holomorphy types for Banach spaces, Proceedings of the Colloqnium on Nuclear Spacer and Ideals in Operator Algebras held in Warsaw, Poland, (1969) (to be published in Studia Mathematica). Zbl0212.14701MR278055
  18. [18] Noverraz, P., Fonctions plurisousharmonique et analytiques dans les espaces vectoriels topologiques complexes, Thesis, Faculte des Sciences de Paris, 1969. Zbl0176.09903MR265628

Citations in EuDML Documents

  1. Chae Soo Bong, Holomorphic germs on Banach spaces
  2. André Hirschowitz, Prolongement analytique en dimension infinie
  3. Luiza A. Moraes, Theorems of the Cartan-Thullen Type and θ -envelope of Holomorphy for Every Holomorphy Type θ
  4. L. Nachbin, Sur quelques aspects récents de l'holomorphie en dimension infinie
  5. Jean-Pierre Vigué, Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornés symétriques
  6. Seán Dineen, Richard M. Timoney, Jean-Pierre Vigué, Pseudodistances invariantes sur les domaines d'un espace localement convexe
  7. Sean Dineen, Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ( U )
  8. Sean Dineen, Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
  9. Jorge Mujica, Spaces of holomorphic mappings on Banach spaces with a Schauder basis

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