Abstract
Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences x = {xk} such that {q(x?)} ? µ{X} for all q ? X. The space µ{X} is given the locally convex topology generated by the semi-norms ?pq(x) = p({q(x?)}), p ? X, q ? M.We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the ?-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}.
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