A new geometrical constant of Banach spaces and the uniform normal structure

摘要

We introduce and study a new geometrical constant γX,ψ of a Banachspace X, by using the notion of ψ-direct sum given in [Y. Takahashi, M. Kato and K.-S. Saito, J. Inequal. Appl. 7 (2002), 179-186]. At first, we characterize uniform non-squareness in terms of γX,ψ.Moreover, we consider Banach spaces having uniformnormal structure.