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A reflexive space of holomorphic functions in infinitely many variables


Authors: Raymundo Alencar, Richard M. Aron and Seán Dineen
Journal: Proc. Amer. Math. Soc. 90 (1984), 407-411
MSC: Primary 46G20; Secondary 32A10
MathSciNet review: 728358
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Abstract: We show the existence of an infinite-dimensional Banach space $ E$ such that $ H(E)$, the space of holomorphic functions on $ E$, endowed with the $ {\tau _\omega }$ topology is reflexive.


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  • [1] R. M. Aron, C. Hervés, and M. Valdivia, Weakly continuous mappings on Banach spaces, J. Funct. Anal. 52 (1983), no. 2, 189–204. MR 707203, 10.1016/0022-1236(83)90081-2
  • [2] P. G. Casazza, Tsirelson’s space, Proceedings of research workshop on Banach space theory (Iowa City, Iowa, 1981) Univ. Iowa, Iowa City, IA, 1982, pp. 9–22. MR 724103
  • [3] Seán Dineen, Holomorphic functions on (𝑐₀,𝑋_{𝑏})-modules, Math. Ann. 196 (1972), 106–116. MR 0300070
  • [4] Seán Dineen, Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on \cal𝐻(𝑈), Ann. Inst. Fourier (Grenoble) 23 (1973), no. 1, 19–54 (English, with French summary). MR 0500153
  • [5] Seán Dineen, Complex analysis in locally convex spaces, North-Holland Mathematics Studies, vol. 57, North-Holland Publishing Co., Amsterdam-New York, 1981. Notas de Matemática [Mathematical Notes], 83. MR 640093
  • [6] J. L. Krivine, Sous-espaces de dimension finie des espaces de Banach réticulés, Ann. of Math. (2) 104 (1976), no. 1, 1–29. MR 0407568
  • [7] R. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, Thesis, Trinity College, Dublin, 1980.
  • [8] B. S. Tsirelson, Not every Banach space contains an imbedding of $ {l_p}$ or $ {c_0}$, Functional Anal. Appl. 8 (1974), 138-141.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0728358-5
Keywords: Reflexivity, weakly sequentially continuous, Tsirelson space
Article copyright: © Copyright 1984 American Mathematical Society