Commun. Korean Math. Soc. 2019; 34(2): 465-475
Online first article January 9, 2019 Printed April 30, 2019
https://doi.org/10.4134/CKMS.c180108
Copyright © The Korean Mathematical Society.
Ji Gao
Community College of Philadelphia
Let $X$ be a Banach space and $X^*$ be its dual. In this paper, we give relationships among some parameters in $X^*$: $\varepsilon$-nonsquareness parameter, $J(\varepsilon,X^*)$; $\varepsilon$-boundary parameter, $Q(\varepsilon, X^*)$; the modulus of smoothness, $\rho_{X^*}(\varepsilon)$; and $\varepsilon$-Pythagorean parameter, $E(\varepsilon, X^*)$, and weak orthogonality parameter, $\omega(X)$ in $X$ that imply uniform norm structure in $X$. Some existing results are extended or approved.
Keywords: normal structure, uniformly non-square space, uniform normal structure
MSC numbers: Primary 46B20
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