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Some equivalent representations of nonsquare constants of spaces with Orlicz norm

✍ Scribed by Ya Qiang Yan

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
139 KB
Volume
274-275
Category
Article
ISSN
0025-584X

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✦ Synopsis

The nonsquare constants in sense of James and Schäffer 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 l Φ , CJ L Φ (Ω) in sense of James and CS l Φ , CS L Φ (Ω) in sense of Schäffer satisfy:

with l Φ and L Φ (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.

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