On a General Class of Geometric Constants and Normal Structure in Banach Spaces

Abstract

In this paper, we establish the lower bounds for the weakly convergent sequence coefficient WCS(X) of a Banach space X, in terms of the family of geometric constants Cλ,p(X), the coefficient of weak orthogonality µ(X) and the generalized García-Falset coefficient R(1, X). By mean of these bounds, we identify some geometrical properties implying normal structure. Moreover, some sufficient conditions which imply uniform normal structure are presented. Our results significantly generalize and improve many known results in the literature.Mathematics Subject Classification (2020): Primary 46B20; Secondary 47H09.