PLB-spaces of holomorphic functions with logarithmic growth conditions

Abstract

Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. In a previous article, the author extended their investigation to the case of holomorphic functions and characterized when spaces over the unit disc w.r.t. weights of polynomial decay are ultrabornological or barrelled. In this note, we prove a similar characterization for the case of weights which tend to zero logarithmically.

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Correspondence to Sven-Ake Wegner.

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Wegner, SA. PLB-spaces of holomorphic functions with logarithmic growth conditions. Arch. Math. 98, 163–172 (2012). https://doi.org/10.1007/s00013-011-0339-x

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Mathematics Subject Classification (2010)

  • Primary 46E10
  • Secondary 46A13
  • 46M18
  • 46M40

Keywords

  • PLB-space
  • Derived projective limit functor
  • Weighted space