Bull. Korean Math. Soc. 2013; 50(2): 417-430
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.417
Copyright © The Korean Mathematical Society.
Zhihua Zhang, Lan Shu, Jun Zheng, and Yuling Yang
University of Electronic Science and Technology of China, University of Electronic Science and Technology of China, Lanzhou University, University of Electronic Science and Technology of China
Let $X$ be a Banach space and $\psi$ a continuous convex function on $\Delta_{K+1}$ satisfying certain conditions. Let $(X\bigoplus X\bigoplus \cdots \bigoplus X)_{\psi}$ be the $\psi$-direct sum of $X$. In this paper, we characterize the $K$ strict convexity, $K$ uniform convexity and uniform non-$l_{1}^{N}$-ness of Banach spaces using $\psi$-direct sums.
Keywords: absolute norm, $K$ strict convexity, $K$ uniform convexity, uniform non-$l_{1}^{N}$-ness
MSC numbers: 46B25, 46b20, 46B99
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