Boundedness and surjectivity in normed spaces
We define the (w* -) boundedness property and the (w* -) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w* -) thickness. We give examples of interesti...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011596 |
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| _version_ | 1849684229240127488 |
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| author | Olav Nygaard |
| author_facet | Olav Nygaard |
| author_sort | Olav Nygaard |
| collection | DOAJ |
| description | We define the (w* -) boundedness property and the (w* -) surjectivity property for sets in normed spaces. We
show that these properties are pairwise equivalent in complete
normed spaces by characterizing them in terms of a category-like
property called (w* -) thickness. We give examples of
interesting sets having or not having these properties. In
particular, we prove that the tensor product of two
w*-thick sets in X** and Y* is a w*-thick subset in L(X,Y)* and obtain as a consequence that the set w*-expBK(l2)* is w*-thick. |
| format | Article |
| id | doaj-art-bd735229b2164fe8b26b536b98a72ed0 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd735229b2164fe8b26b536b98a72ed02025-08-20T03:23:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132314916510.1155/S0161171202011596Boundedness and surjectivity in normed spacesOlav Nygaard0Department of Mathematics, Agder University College, Servicebox 422, Kristiansand 4604, NorwayWe define the (w* -) boundedness property and the (w* -) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w* -) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of two w*-thick sets in X** and Y* is a w*-thick subset in L(X,Y)* and obtain as a consequence that the set w*-expBK(l2)* is w*-thick.http://dx.doi.org/10.1155/S0161171202011596 |
| spellingShingle | Olav Nygaard Boundedness and surjectivity in normed spaces International Journal of Mathematics and Mathematical Sciences |
| title | Boundedness and surjectivity in normed spaces |
| title_full | Boundedness and surjectivity in normed spaces |
| title_fullStr | Boundedness and surjectivity in normed spaces |
| title_full_unstemmed | Boundedness and surjectivity in normed spaces |
| title_short | Boundedness and surjectivity in normed spaces |
| title_sort | boundedness and surjectivity in normed spaces |
| url | http://dx.doi.org/10.1155/S0161171202011596 |
| work_keys_str_mv | AT olavnygaard boundednessandsurjectivityinnormedspaces |