On some normability conditions

Terzioglu T., Yurdakul M., Zahariuta V.

MATHEMATISCHE NACHRICHTEN, vol.278, no.14, pp.1714-1725, 2005 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 278 Issue: 14
  • Publication Date: 2005
  • Doi Number: 10.1002/mana.200310336
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1714-1725


Various normability conditions of locally convex spaces (including Vogt interpolation classes DN phi and Omega phi as well as quasi- and asymptotic normability) are investigated. In particular, it is shown that on the class of Schwartz spaces the property of asymptotic normability coincides with the property GS, which is a natural generalization of Gelfand-Shilov countable normability (cf. [9, 25], where the metrizable case was treated). It is observed also that there are certain natural duality relationships among some of normability conditions. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.