Generalized von Neumann-Jordan and James Constants for Quasi-Banach Spaces

摘要

The generalized von Neumann-Jordan constant C_(NJ)~((p)) (B) and the James constant J(B) for a quasi-Banach space were introduced in [7]. In this note, it is shown that C_(NJ)~((p)) (B) ≤ 2 for any quasi-Banach space B and C_(NJ)~((p)) (B) < 2 if and only if B is uniformly non-square. Along with relationship between J(B) and C_(NJ)~((p)) (B), the criterion for the uniformly smooth quasi-Banach space is also established.