The Mackey convergence condition for spaces with webs
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 t...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000559 |
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| _version_ | 1832545624856199168 |
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| author | Thomas E. Gilsdorf |
| author_facet | Thomas E. Gilsdorf |
| author_sort | Thomas E. Gilsdorf |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0d8acd2e014446bc87a06086edc69510 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0d8acd2e014446bc87a06086edc695102025-02-03T07:25:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111347348310.1155/S0161171288000559The Mackey convergence condition for spaces with websThomas E. Gilsdorf0Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164, USAIf 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.http://dx.doi.org/10.1155/S0161171288000559compatible webfast complete spaceMackey convergent sequenceinductive limit. |
| spellingShingle | Thomas E. Gilsdorf The Mackey convergence condition for spaces with webs International Journal of Mathematics and Mathematical Sciences compatible web fast complete space Mackey convergent sequence inductive limit. |
| title | The Mackey convergence condition for spaces with webs |
| title_full | The Mackey convergence condition for spaces with webs |
| title_fullStr | The Mackey convergence condition for spaces with webs |
| title_full_unstemmed | The Mackey convergence condition for spaces with webs |
| title_short | The Mackey convergence condition for spaces with webs |
| title_sort | mackey convergence condition for spaces with webs |
| topic | compatible web fast complete space Mackey convergent sequence inductive limit. |
| url | http://dx.doi.org/10.1155/S0161171288000559 |
| work_keys_str_mv | AT thomasegilsdorf themackeyconvergenceconditionforspaceswithwebs AT thomasegilsdorf mackeyconvergenceconditionforspaceswithwebs |