PLB-spaces of holomorphic functions with logarithmic growth conditions

Sven Ake Wegner

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)163-172
Number of pages10
JournalArchiv der Mathematik
Volume98
Issue number2
DOIs
Publication statusPublished - Feb 2012
Externally publishedYes

Fingerprint

Growth Conditions
Countable
Analytic function
Logarithmic
Polynomial Decay
Projective Limit
Inductive Limit
Spaces of Continuous Functions
Unit Disk
Banach space
Tend
Zero

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

PLB-spaces of holomorphic functions with logarithmic growth conditions. / Wegner, Sven Ake.

In: Archiv der Mathematik, Vol. 98, No. 2, 02.2012, p. 163-172.

Research output: Contribution to journalArticle

Wegner, Sven Ake. / PLB-spaces of holomorphic functions with logarithmic growth conditions. In: Archiv der Mathematik. 2012 ; Vol. 98, No. 2. pp. 163-172.
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