Some equivalent representations of nonsquare constants of spaces with Orlicz norm

Abstract

The nonsquare constants in sense of James and Schaffer have the interrelation: CJ (X) · CS(X) = 2 for a Banach space X. For Orlicz sequence and function spaces equipped with Luxemburg norm, the representation of CJ and CS were obtained ([6], [7]). In this paper, we show that the nonsquare constants CJ (lΦ), CJ(LΦ(Ω)) in sense of James and CS(lΦ), CS(LΦ(Ω)) in sense of Schaffer satisfy: (i) if ϕ(t) is concave, then (ii) if ϕ(t) is convex, then with lΦ and LΦ(Ω) being the Orlicz sequence space and function space generated by the N-function Φ(u) with Orlicz norm, ϕ(t) being the right derivative of Φ. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)