Some remarks about Mackey convergence

Józef Burzyk and Thomas E. Gilsdorf

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-6

Abstract:

In this paper, we examine Mackey convergence with respect to K -convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K ; there are spaces having K - convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence condition, is barrelled, but is not bornological; and if a space satisfies the biackey convergence condition and every sequentially continuous seminorm is continuous, then the space is bornological.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:138625

DOI: 10.1155/S0161171295000846

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