Abstract and Applied Analysis

On Semi-Uniform Kadec-Klee Banach Spaces

Satit Saejung and Ji Gao

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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).

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 652521, 12 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620783

Digital Object Identifier
doi:10.1155/2010/652521

Mathematical Reviews number (MathSciNet)
MR2726617

Zentralblatt MATH identifier
1208.46018

Citation

Saejung, Satit; Gao, Ji. On Semi-Uniform Kadec-Klee Banach Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 652521, 12 pages. doi:10.1155/2010/652521. https://projecteuclid.org/euclid.aaa/1288620783


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