Bounde Reinhardt domains in Banach spaces

T. Barton; S. Dineen; R. Timoney

Compositio Mathematica (1986)

  • Volume: 59, Issue: 3, page 265-321
  • ISSN: 0010-437X

How to cite


Barton, T., Dineen, S., and Timoney, R.. "Bounde Reinhardt domains in Banach spaces." Compositio Mathematica 59.3 (1986): 265-321. <>.

author = {Barton, T., Dineen, S., Timoney, R.},
journal = {Compositio Mathematica},
keywords = {bounded Reinhardt domains},
language = {eng},
number = {3},
pages = {265-321},
publisher = {Martinus Nijhoff Publishers},
title = {Bounde Reinhardt domains in Banach spaces},
url = {},
volume = {59},
year = {1986},

AU - Barton, T.
AU - Dineen, S.
AU - Timoney, R.
TI - Bounde Reinhardt domains in Banach spaces
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 59
IS - 3
SP - 265
EP - 321
LA - eng
KW - bounded Reinhardt domains
UR -
ER -


  1. [1] R. Alencar, R.M. Aron and S.O. Dineen: A reflexive space of holomorphic functions in infinitely many variables. Proc. A.M.S. 96 (1984) 407-411. Zbl0536.46015MR728358
  2. [2] T.J. Barton: Bounded Reinhardt domains in complex Banach spaces Dissertation, Kent State University (1984). 
  3. [3] R. Braun, W. Kaup and H. Upmeier: On the automorphisms of circular and Reinhardt domains in complex Banach spaces. Manuscripta Math.25 (1978) 97-133. Zbl0398.32001MR500878
  4. [4] E. Cartan: Sur les domaines bornés homogènes de l'espace de n variàbles complexes. Abh. Math. Sem. Univ. Hamburg11 (1935) 116-162. Zbl0011.12302JFM61.0370.03
  5. [5] H. Cartan: Les fonctions de deux variàbles complexes et le problème de la représentation analytique. J. Math. Pures Appl., 9e série, 10 (1931) 1-144. JFM57.0387.01
  6. [6] P.G. Casazza: Tsirelsohn's space. Proc. of the Research Workshop on Banach Space Theory, University of Iowa, Bor-Luh Lin, ed., pp. 9-22 (1981). Zbl0505.46014MR724103
  7. [7] P.G. Casazza: Finite dimensional decompositions in Banach spaces. Preprint. MR840692
  8. [8] P.G. Casazza, W.B. Johnson and L. Tzafriri: On Tsirelsohn's space. Preprint. 
  9. [9] S. Dineen: Complex analysis in locally convex spaces. North Holland Math. Studies, 57 (1981). Zbl0484.46044MR640093
  10. [10] D. Drucker: Exceptional Lie algebras and the structure of hermitian symmetric spaces. Memoirs208, Amer. Math. Soc., Providence (1978). Zbl0395.17009
  11. [11] T. Figiel and W.J. Johnson: A uniformly convex Banach space which contains no lp. Comp. Math.29 (1974) 179-190. Zbl0301.46013MR355537
  12. [12] T. Franzoni: and E. Vesentini: Holomorphic maps and invariant distances. North Holland Math. Studies, 40 (1980). Zbl0447.46040MR563329
  13. [13] L. Harris: Bounded symmetric homogeneous domains in infinite dimensional spaces. In Lecture Notes364. Springer-Verlag, New York-Heidelberg -Berlin, 1974 (13-40). Zbl0293.46049MR407330
  14. [14] L. Harris: A generalization of C*-algebras. Proc. Lond. Math. Soc. (3) 42 (1981) 331-361. Zbl0476.46054MR607306
  15. [15] S. Helgason: Differential geometry, Lie groups, and symmetric spaces. Pure and Applied Math.80. Academic Press, New York- San Francisco-London (1978). Zbl0451.53038MR514561
  16. [16] J.E. Humphreys: Introduction to Lie algebras and representation theory. GTM 9, Springer-Verlag, New York-Heidelberg-Berlin (1972). Zbl0254.17004MR323842
  17. [17] W.B. Johnson: A reflexive Banach space which is not sufficiently euclidean. Studia Math.55 (1976) 201-205. Zbl0362.46015MR430756
  18. [18] W. Kaup: Algebraic characterization of symmetric complex Banach manifolds. Math. Ann.228 (1977) 39-64. Zbl0335.58005MR454091
  19. [19] W. Kaup: Contractive projections on Jordan C*-algebras and generalizations. Math. Scand.54 (1984) 95-100. Zbl0578.46066MR753066
  20. [20] W. Kaup: A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z.183 (1983) 503-529. Zbl0519.32024MR710768
  21. [21] W. Kaup and H. Upmeier: Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc. A.M.S.58 (1978) 129-133. Zbl0337.32012MR422704
  22. [22] J. Lindenstrauss and L. Tzafriri: Classical Banach spaces I. Ergebnisse 92, Springer-Verlag, New York- Heidelberg-Berlin (1977). Zbl0362.46013MR500056
  23. [23] O. Loos: Symmetric spaces II, compact spaces and classsification. Benjamin, New York (1969). Zbl0175.48601MR239006
  24. [24] O. Loos: Bounded symmetric domains and Jordan pairs. Lecture notes, University of California at Irvine (1977). 
  25. [25] G.D. Mostow: Lectures on Lie groups and Lie algebras. Lecture notes, Yale University (1968). 
  26. [26] L.L. Stachó: A short proof that the biholomorphic automorphisms of the unit ball in certain Lp spaces are linear. Acta Sci. Math., 41 (1979) 381-383. Zbl0432.58006MR555432
  27. [27] L.L. Stachó, A projection principle concerning biholomorphic automorphisms. Acta Sci. Math., 44 (1982) 99-124. Zbl0505.58008MR660517
  28. [28] T. Sunada: Holomorphic equivalence problem for bounded Reinhardt domains. Math. Ann.235 (1978) 111-128. Zbl0357.32001MR481064
  29. [29] P. Thullen: Die Invarianz des Mittelpunktes von Kreiskorpen. Math. Ann.104 (1931) 244-259. Zbl0001.02303MR1512662JFM57.0385.03
  30. [30] B.S. Tsirelsohn: Not every Banach space contains lp or c0. Func. Ann. Appl.8 (1974) 138-141. Translated from Russian. Zbl0296.46018
  31. [31] J.P. Vigué: Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornés symétriques. Ann. Scien . Ec. Norm. Sup., 4e série, 9 (1976) 203-282. Zbl0316.32007MR430335
  32. [32] J.P. Vigué: Les domaines bornés symétriques d'un espace de Banach complexe et les systémes triples de Jordan. Math. Ann., 229 (1977) 223-231. Zbl0344.32024MR447648
  33. [33] J.P. Vigué: Automorphismes analytiques des produit continus de domaines bornés. Ann. Scien. Ec. Norm. Sup., 4e série, 11 (1978) 229-246. Zbl0405.32007MR510550
  34. [34] J.P. Vigué: Sur la dècomposition d'un domaine borné symmétrique en produit continu de domaines bornés symétriques irréductibles. Ann. Scien. Ec. Norm. Sup., 4e série, 14 (1981) 453-463. Zbl0487.32020MR654207
  35. [35] J.P. Vigué: Automorphismes analytiques d'un domaine de Reinhardt borné d'un espace de Banach a base. Ann. de l'Inst. Fourier, 34, 2 (1984), 67-87. Zbl0525.32027MR746496
  36. [36] J.P. Vigué and J.M. Isidro, Sur la topologie du group des automorphismes analytiques d'un domaine circlé borné. Bull. Soc. Mat. Fr., 106 (1982) 417-426. Zbl0546.32012MR688200
  37. [37] J.A. Wolf: Fine structure of Hermitian symmetric spaces. In Symmetric spaces. Marcel Dekker, New York (1972) 271-357. Zbl0257.32014MR404716

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