On Semi-Uniform Kadec-Klee Banach Spaces
Inspired by the concept of U-spaces introduced by Lau, (1978), we introduced the class of semi-uniform Kadec-Klee spaces, which is a uniform version of semi-Kadec-Klee spaces studied by Vlasov, (1972). This class of spaces is a wider subclass of spaces with weak normal structure and hence generalize...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/652521 |
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| Summary: | Inspired by the concept of U-spaces introduced by Lau, (1978), we
introduced the class of semi-uniform Kadec-Klee spaces, which is a uniform
version of semi-Kadec-Klee spaces studied by Vlasov, (1972). This class of spaces
is a wider subclass of spaces with weak normal structure and hence generalizes
many known results in the literature. We give a characterization for a certain
direct sum of Banach spaces to be semi-uniform Kadec-Klee and use this result
to construct a semi-uniform Kadec-Klee space which is not uniform Kadec-Klee. At the end of the paper, we give a remark concerning the uniformly
alternative convexity or smoothness introduced by Kadets et al., (1997). |
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| ISSN: | 1085-3375 1687-0409 |