Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Characterizations of geometrical properties of Banach spaces using $\psi$-direct sums

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

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-$l_{1}^{N}$-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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