On Semi-Uniform Kadec-Klee Banach Spaces

Satit Saejung and Ji Gao

Abstract and Applied Analysis, 2010, vol. 2010, 1-12

Abstract:

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).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:652521

DOI: 10.1155/2010/652521

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