Strict convexity and smoothness of normed spaces

Junzo Wada
Strict Convexity and Smoothness of Normed Spaces Junzo WADA V. L. Klee [II] 15 and M. M. Day [6] have considered various problems on strict convexity and smoothness of normed spaces. In his paper, Day [6] raised several questions. Two of these are the following: (1) Is any L Γ space strictly convexiίiable ? (2) Is there a nonreflexive nonsparable scm space? In this paper, we consider these questions. In § 2 we deal with spaces of bounded continuous functions and consider strict convexity and
more » ... ct convexity and smoothness on these spaces. In § 3 we give a partial answer to the first question, and in § 4 we give an answer to the second, by showing an example of a nonreflexive nonseparable scm space. 1) Numbers in bracket refer to the references cited at the end of the paper.
doi:10.18910/10810 fatcat:fzm3hwdnlnbj5j37xtprme33gu