On Kadec Norms and Asplund Spaces

Abstract

This paper is focused on some properties that linked with renorming theory in connection with the Kadec norms. More important ramification of Kadec norms have been seen. A succinct introduction to Kadec- klee norms and Asplund spaces is given and provide the fascinating connection between w-w*- Kadec –Klee norms and Asplund spaces. We study nearly about the problem whether the existence of a KK* renorming of X* implies that X is an Asplund space? which has apparently been posed by Godefroy, [i, ii].