Some forms of the closed graph theorem

Abstract

In this paper we shall establish some forms of the closed graph theorem for locally convex spaces, using the approach of Pták(17). Our interest is in classifying pairs of locally convex spaces (E, F) which have the property that every closed graph linear mapping T: E → F is continuous; if (E, F) has this property then we shall say that (E, F) is in the class ℒ if is a particular class of locally convex spaces then ℒ() is the class of all E such that (E, F)∈ℒ for all F ∈ .