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http://dx.doi.org/10.4134/BKMS.2013.50.2.417

CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS  

Zhang, Zhihua (School of Mathematical Sciences University of Electronic Science and Technology of China)
Shu, Lan (School of Mathematical Sciences University of Electronic Science and Technology of China)
Zheng, Jun (School of Mathematics and Statistics Lanzhou University)
Yang, Yuling (School of Mathematical Sciences University of Electronic Science and Technology of China)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 417-430 More about this Journal
Abstract
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-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.
Keywords
absolute norm; K strict convexity; K uniform convexity; uniform non-$l^N_1$-ness;
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