Boundedness and surjectivity in normed spaces

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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Main Author: Olav Nygaard
Format: Article
Language:English
Published: Hindawi Limited 2002-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171202011596
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spelling doaj-bd735229b2164fe8b26b536b98a72ed02020-11-25T00:48:04ZengHindawi LimitedInternational 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
collection DOAJ
language English
format Article
sources DOAJ
author Olav Nygaard
spellingShingle Olav Nygaard
Boundedness and surjectivity in normed spaces
International Journal of Mathematics and Mathematical Sciences
author_facet Olav Nygaard
author_sort Olav Nygaard
title Boundedness and surjectivity in normed spaces
title_short 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_sort boundedness and surjectivity in normed spaces
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2002-01-01
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.
url http://dx.doi.org/10.1155/S0161171202011596
work_keys_str_mv AT olavnygaard boundednessandsurjectivityinnormedspaces
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