On Semi-Uniform Kadec-Klee Banach Spaces

Abstract EN

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).