A study of some classes of topological vector spaces

Skanes, Glen (1976) A study of some classes of topological vector spaces. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this dissertation, we study two important classes of locally convex spaces in great detail. The first one is the class of (DF)-spaces, introduced by GROTHENDIECK as a prototype of duals of (F)-spaces. A non-locally convex analogue of these spaces is also discussed. The second one is the class of Schwartz spaces. The role of certain Banach spaces as "universal" to the "variety" of all Schwartz spaces in investigated. Finally, co-Schwartz spaces are introduced in a fashion analogous to the study of co-nuclear spaces from that of nuclear spaces. Several counter-examples are provided.

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