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On ∧-Mackey convergence in locally convex spaces

Published online by Cambridge University Press:  24 October 2008

Jan H. Fourie
Jan H. Fourie
Affiliation:
Department of Mathematics, Potchefstroom University, Potchefstroom 2520, South Africa
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In this note we introduce the concepts of Λ-Mackey sequence, Λ-Mackey convergence property, Λ-Schwartz family and associated Λ-Schwartz family and consider some applications of these to locally convex spaces. Hereby Λ denotes a Banach sequence space with the AK-property — the results of this paper generalize those in [4] where the case Λ = I1 is considered. We obtain a dual characterization of those locally convex spaces which satisfy the Λ-Mackey convergence property and characterize the dual Λ-Schwartz spaces in terms of the SM-property which is introduced in [10]. Finally, necessary and sufficient condition for a locally convex space to be ultra-bornological is proved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 495 - 500
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

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