Academic Editor: S. Reich
Copyright © 2010 Satit Saejung and Ji Gao. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).