The Mackey Convergence Condition for Spaces with Webs

Thomas E. Gilsdorf

doi:10.1155/S0161171288000559

The Mackey Convergence Condition for Spaces with Webs

Thomas E. Gilsdorf

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.

Original language	English
Pages (from-to)	473-483
Number of pages	11
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	11
Issue number	3
DOIs	https://doi.org/10.1155/S0161171288000559
State	Published - 1988

Keywords

Compatible web
Mackey convergent sequence
fast complete space
inductive limit

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10.1155/S0161171288000559

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abstract = "If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.",

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AB - If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.

KW - Compatible web

KW - Mackey convergent sequence

KW - fast complete space

KW - inductive limit

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JO - International Journal of Mathematics and Mathematical Sciences

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SN - 0161-1712

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ER -

The Mackey Convergence Condition for Spaces with Webs

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Keywords

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