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On Semi-Uniform Kadec-Klee Banach Spaces

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  • Satit Saejung
  • Ji Gao

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).

Suggested Citation

  • Satit Saejung & Ji Gao, 2010. "On Semi-Uniform Kadec-Klee Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, October.
    • Handle: RePEc:hin:jnlaaa:652521
    DOI: 10.1155/2010/652521
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