[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180108

RESEARCH ON NORMAL STRUCTURE IN A BANACH SPACE VIA SOME PARAMETERS IN ITS DUAL SPACE

Gao, Ji (Department of Mathematics Community College of Philadelphia)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 465-475 More about this Journal

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;

Citations & Related Records

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