Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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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.

Research on normal structure in a Banach space via some parameters in its dual space

Ji Gao

Community College of Philadelphia

Abstract

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