Banas-Hajnosz-Wedrychowicz type modulus of convexity and normal structure in Banach spaces (Q721192)

The author presents some sufficient conditions for a Banach space to have uniform normal structure in terms of inequalities involving the coefficients \(SY_X(\varepsilon)\) defined by \textit{S. Saejung} and \textit{J. Gao} [Nonlinear Funct. Anal. Appl. 21, No. 4, 717--725 (2016; Zbl 1431.46008)], the coefficient of weak orthogonality \(w(X)\) defined by \textit{B. Sims} [Bull. Aust. Math. Soc. 49, No. 3, 523--528 (1994; Zbl 0807.47047)], and the coefficient \(R(1,X)\) defined by \textit{T. Domínguez Benavides} [Houston J. Math. 22, No. 4, 835--849 (1996; Zbl 0873.46012)]. Reviewer's remark: When reading the proofs of the theorems, the reader may find it useful to keep in mind that, for superreflexive Banach spaces, the values of the three coefficients mentioned above remain unchanged if \(X\) is replaced by an ultrapower of \(X\).