On some normability conditions
Terzioğlu, Tosun and Yurdakul, Murat and Zakharyuta, Vyacheslav (2005) On some normability conditions. Mathematische nachrichten, 278 (14). pp. 1714-1725. ISSN 0025-584X
Official URL: http://dx.doi.org/10.1002/mana.200310336
Various normability conditions of locally convex spaces (including Vogt interpolation classes DN and 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.
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