Arkiv för Matematik

  • Ark. Mat.
  • Volume 15, Number 1-2 (1977), 87-91.

An example of a nuclear space in infinite dimensional holomorphy

Philip J. Boland

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LetU be an open subset of a complex locally convex space E, and H(U) the space of holomorphic functions from U to C. If the dual E′ of E is nuclear with respect to the topology generated by the absolutely convex compact subsets of E, then it is shown that H(U) endowed with the compact open topology is a nuclear space. In particular, if E is the strong dual of a Fréchet nuclear space, then H(U) is a Fréchet nuclear space.

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Ark. Mat., Volume 15, Number 1-2 (1977), 87-91.

Received: 27 October 1975
First available in Project Euclid: 31 January 2017

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1977 © Institut Mittag-Leffler


Boland, Philip J. An example of a nuclear space in infinite dimensional holomorphy. Ark. Mat. 15 (1977), no. 1-2, 87--91. doi:10.1007/BF02386034.

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  • Boland, P. J., Holomorphic functions on nuclear spaces, Trans. Amer. Math. Soc., 209 (1975), 275–281.
  • Boland, P. J., Malgrange theorem for entire functions on nuclear spaces, Proceedings on infinite dimensional holomorphy, Lecture Notes in Mathematics 364 (1974), 135–144.
  • Pietsch, A., Nuclear locally convex spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66, Springer Verlag, New York, 1972.