Abstract
Let Φ(u) be an N-function and let \(L^{(\Phi)}[0, 1]\) and \(L^{\Phi}[0, 1]\) be the Orlicz function spaces equipped with the gauge norm and the Orlicz norm respectively. The author refines some results on the upper bounds of the weak convergent sequence coefficients \(WCS(L^{(\Phi)}[0, 1])\) and \(WCS(L^{\Phi}[0, 1])\) given in [8] and [7, Ch.3.2]. Theorems 1 and 2 are given in Section 2. Several examples, given in Section 3, are used to make comments upon the papers of Yan [11], [12] and [13].
Keywords Orlicz space, WCS coefficient and normal structure coefficient
Mathematics Subject Classification (2000) 46B30
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Ren, Z.D. On the upper bounds of WCS coefficients in Orlicz function spaces. Rend. Circ. Mat. Palermo 57, 125–140 (2008). https://doi.org/10.1007/s12215-008-0007-6
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DOI: https://doi.org/10.1007/s12215-008-0007-6