Geodesic
On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm
Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 204-224

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Let ${{l}^{\Phi }}$ and ${{L}^{\Phi }}\left( \Omega\right)$ be the Orlicz sequence space and function space generated by $N$ -function $\Phi (u)$ with Orlicz norm. We give equivalent expressions for the nonsquare constants ${{C}_{J}}\left( {{l}^{\Phi }} \right),\,{{C}_{J}}\left( {{L}^{\Phi }}\left( \Omega\right) \right)$ in sense of James and ${{C}_{S}}\left( {{l}^{\Phi }} \right),\,{{C}_{S}}\left( {{L}^{\Phi }}\left( \Omega\right) \right)$ in sense of Schäffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces ${{l}^{\Phi }}$ and ${{L}^{\Phi}}\left(\Omega \right)$ .
DOI : 10.4153/CJM-2003-009-1
Mots-clés : 46E30, James nonsquare constant, Schäffer nonsquare constant, Orlicz sequence space, Orlicz function space 
Yan, Yaqiang. On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm. Canadian journal of mathematics, Tome 55 (2003) no. 1, pp. 204-224. doi: 10.4153/CJM-2003-009-1
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[1] [1] Chen, S. T., Non-squareness of Orlicz spaces. Chinese Ann.Math. Ser. A 6 (1985), 619–624. Google Scholar

[2] [2] Chen, S. T., Geometry of Orlicz spaces. Dissertation Math. 356 (1996), 17–23. Google Scholar

[3] [3] Cui, Y. A., Weakly convergent sequence coefficient in Köthe sequence spaces. Proc. Amer.Math. Soc. (1) 126 (1998), 195–210. Google Scholar

[4] [4] Gao, J. and Lau, K. S., On the geometry of spheres in normed linear spaces. J. Austral.Math. Soc. Ser. A 48 (1990), 101–112. Google Scholar

[5] [5] Hudzik, H., Uniformly non-l(1) n Orlicz spaces with Luxemburg norm. Studia Math. 81 (1985), 271–284. Google Scholar

[6] [6] Ji, D. H. and Wang, T. F., Nonsquare constants of normed spaces. Acta. Sci. Math. (Szeged) 59 (1994), 719–723. Google Scholar

[7] [7] Ji, D. H. and Zhan, D. P., Some equivalent representations of nonsquare constants and its applications. Northeast. Math. J. (4) 15 (1999), 439–444. Google Scholar

[8] [8] Krasnoselskiĭ, M. A. and Rutickiĭ, Ya. B., Convex Functions and Orlicz Spaces. Noordhoff, Groningen, 1961. Google Scholar

[9] [9] Rao, M. M. and Ren, Z. D., Packing in Orlicz sequence spaces. Studia Math. 126 (1997), 235–251. Google Scholar

[10] [10] Ren, Z. D., Nonsquare constants of Orlicz spaces. Lecture Notes in Pure and Applied Math. 186 (1997), 179–197. Google Scholar

[11] [11] Wang, T. F., Packing constants of Orlicz sequence spaces. Chinese Ann.Math. Ser. A 8 (1987), 508–513. Google Scholar

[12] [12] Wang, Y. W. and Chen, S. T., Non squareness, B-convexity and flatness of Orlicz spaces. Comment. Math. Prace. Mat. 28 (1988), 155–165. Google Scholar

[13] [13] Yan, Y. Q., Some results on packing in Orlicz sequence spaces. Studia Math. (1) 147 (2001), 73–88. Google Scholar

[14] [14] Yan, Y. Q., Computation of Nonsquare Constants of Orlicz Spaces. J. Austral. Math. Soc., to appear. Google Scholar

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