Bounded sets in fast complete inductive limits
Let E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117128400065X |
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| _version_ | 1850213878762307584 |
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| author | Jan Kucera Carlos Bosch |
| author_facet | Jan Kucera Carlos Bosch |
| author_sort | Jan Kucera |
| collection | DOAJ |
| description | Let E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed. |
| format | Article |
| id | doaj-art-876632429307428f9a52fcd844c0ea14 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-876632429307428f9a52fcd844c0ea142025-08-20T02:09:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017361561710.1155/S016117128400065XBounded sets in fast complete inductive limitsJan Kucera0Carlos Bosch1Department of Mathematics, Washington State University, Pullman 99164, Washington, USADepartment of Mathematics, Washington State University, Pullman 99164, Washington, USALet E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.http://dx.doi.org/10.1155/S016117128400065Xinductive limit of locally convex spacesfast complete spacewebbed spacebounded set. |
| spellingShingle | Jan Kucera Carlos Bosch Bounded sets in fast complete inductive limits International Journal of Mathematics and Mathematical Sciences inductive limit of locally convex spaces fast complete space webbed space bounded set. |
| title | Bounded sets in fast complete inductive limits |
| title_full | Bounded sets in fast complete inductive limits |
| title_fullStr | Bounded sets in fast complete inductive limits |
| title_full_unstemmed | Bounded sets in fast complete inductive limits |
| title_short | Bounded sets in fast complete inductive limits |
| title_sort | bounded sets in fast complete inductive limits |
| topic | inductive limit of locally convex spaces fast complete space webbed space bounded set. |
| url | http://dx.doi.org/10.1155/S016117128400065X |
| work_keys_str_mv | AT jankucera boundedsetsinfastcompleteinductivelimits AT carlosbosch boundedsetsinfastcompleteinductivelimits |