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

Title & Authors
CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS
Zhang, Zhihua; Shu, Lan; Zheng, Jun; Yang, Yuling;

Abstract
Let X be a Banach space and $\small{{\psi}}$ a continuous convex function on $\small{{\Delta}_{K+1}}$ satisfying certain conditions. Let $\small{(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}}$ be the $\small{{\psi}}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$\small{l^N_1}$-ness of Banach spaces using $\small{{\psi}}$-direct sums.
Keywords
absolute norm;K strict convexity;K uniform convexity;uniform non-$\small{l^N_1}$-ness;
Language
English
Cited by
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