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2010 On Semi-Uniform Kadec-Klee Banach Spaces
Satit Saejung, Ji Gao
Abstr. Appl. Anal. 2010: 1-12 (2010). DOI: 10.1155/2010/652521


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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Satit Saejung. Ji Gao. "On Semi-Uniform Kadec-Klee Banach Spaces." Abstr. Appl. Anal. 2010 1 - 12, 2010.


Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1208.46018
MathSciNet: MR2726617
Digital Object Identifier: 10.1155/2010/652521

Rights: Copyright © 2010 Hindawi

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