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Keywords:
Orlicz space; $N$-function; index function; Riesz angle
Orlicz space; $N$-function; index function; Riesz angle
Summary:
We introduce some practical calculation of the Riesz angles in Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For an $N$-function $\Phi(u)$ whose index function is monotonous, the exact value $a(l^{(\Phi)})$ of the Orlicz sequence space with Luxemburg norm is $a(l^{(\Phi)})=2^{\frac{1}{C^0_{\Phi}}}$ or $a(l^{(\Phi)})=\frac{\Phi^{-1}(1)}{\Phi^{-1}(\frac{1}{2})}$. The Riesz angles of Orlicz space $l^\Phi$ with Orlicz norm has the estimation $\max (2\beta^0_{\Psi}, 2\beta '_{\Psi})\leq a(l^{\Phi}) \leq\frac{2}{\theta^0_{\Phi}}$.
References:
[1] Benavides T.D., Rodriguez R.J.: Some geometric coefficients in Orlicz sequence spaces. Nonlinear Anal. 20 (1993), 349-358. MR 1206424 | Zbl 0805.46009
[2] Borwein J.M., Sims B.: Non-expansive mappings on Banach lattices and related topics. Houston J. Math. 10 (1984), 339-356. MR 0763236 | Zbl 0584.47055
[3] Chen S.T.: Geometry of Orlicz spaces. Dissertationes Mathematicae, Warszawa, 1996. MR 1410390 | Zbl 1089.46500
[4] Cui Y., Hudzik H., Li Y.: On the Garcia-Falset coefficient in some Banach sequence spaces. Function Spaces and Applications, 1999. MR 1772119 | Zbl 0962.46011
[5] Lindenstrauss J., Tzafriri L.: Classical Banach Spaces. (I) and (II), Berlin-Heidelberg-New York, Springer-Verlag, 1977 and 1979. MR 0500056 | Zbl 0852.46015
[6] Maligranda L.: Orlicz Spaces and Interpolation. Seminars in Mathematics 5, Univ. Estadual de Campinas, Capinas SP Brasil, 1989. MR 2264389 | Zbl 0874.46022
[7] Semenov E.M.: A new interpolation theorem (in Russian). Funkctional. Anal. i Prilozhen. 2 (1968), 158-169. MR 0236694
[8] Simonenko I.B.: Interpolation and extrapolation of linear operators in Orlicz spaces. Mat. Sb. 63 (1964), 536-553. MR 0199696
[9] Rao M.M., Ren Z.D.: Packing in Orlicz sequence spaces. Studia Math. 126 (1997), 235-251. MR 1475921
[10] Yan Y.Q.: Some results on packing in Orlicz sequence spaces. Studia Math. 147 (2001), 73-88. MR 1853478 | Zbl 0986.46004
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