Hudzik, Henryk; Wang, Baoxiang Approximate compactness in Orlicz spaces. (English) Zbl 0913.46032 J. Approximation Theory 95, No. 1, 82-89 (1998). Let \(M\) be a convex \(N\)-function and let \(\ell^M\) be the Orlicz sequence space with Luxemburg norm, \(L^M\) the Orlicz space with Luxemburg norm or with Orlicz norm of functions over a Lebesgue measurable set \(\Omega\subset \mathbb{R}\) of finite measure. It is proved that \(\ell^M\) is approximatively compact if and only if it is reflexive and \(L^M\) is approximatively compact if and only if it is reflexive and rotund. Reviewer: J.Musielak (Poznań) Cited in 1 ReviewCited in 18 Documents MSC: 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46A45 Sequence spaces (including Köthe sequence spaces) 46B25 Classical Banach spaces in the general theory Keywords:Orlicz function space; approximately compact space; reflexive space; rotund space; Orlicz sequence space with Luxemburg norm PDFBibTeX XMLCite \textit{H. Hudzik} and \textit{B. Wang}, J. Approx. Theory 95, No. 1, 82--89 (1998; Zbl 0913.46032) Full Text: DOI References: [1] Braess, D., Nonlinear Approximation Theory (1986), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0656.41001 [2] Chen, S. T., Geometry of Orlicz spaces, Dissertationes Math., 356 (1996) · Zbl 1089.46500 [3] Chen, S. T.; Hudzik, H.; Kamińska, A., Support functionals and smooth points in Orlicz function spaces equipped with the Orlicz norm, Math. Japon., 39, 271-279 (1994) · Zbl 0804.46035 [4] Chen, S. T.; Lin, B. L.; Yu, X. T., Rotund reflexive Orlicz spaces are fully convex, Contemp. Math., 85, 79-86 (1989) [5] Fan, Ky; Glicksberg, I., Fully convex linear spaces, Proc. Nat. Acad. Sci. U.S.A., 41, 947-953 (1955) · Zbl 0065.34501 [6] Hudzik, H., Uniformly non-\(l^{(1)}_n\) Orlicz spaces with Luxemburg norm, Studia Math., 81, 271-284 (1985) · Zbl 0591.46018 [7] Kamińska, A., On uniform convexity of Orlicz spaces, Indag. Math., 44, 27-36 (1982) · Zbl 0489.46025 [8] Krasnoselskiı, M. A.; Rutickiı, Ya. B., Convex Functions and Orlicz Spaces (1961), Nordhoff: Nordhoff Groningen [9] Luxemburg, W. A.J., Banach Functions Spaces (1955) · Zbl 0068.09204 [10] Maligranda, L., Orlicz Spaces and Interpolation. Orlicz Spaces and Interpolation, Seminars in Mathematics, 5 (1989) · Zbl 0874.46022 [11] Musielak, J., Orlicz Spaces and Modular Spaces. Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, 1034 (1983), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0557.46020 [12] Rao, M. M.; Ren, Z. D., Theory of Orlicz Spaces (1991), Dekker: Dekker New York/Basel/Hong Kong · Zbl 0724.46032 [13] Wang, T. F.; Zhang, Y. F.; Wang, B. X., Full rotundity of Orlicz spaces, J. Harbin Normal Univ., 5, 19-21 (1989) · Zbl 0971.46511 [14] Wang, B. X., Support funcionals and its applications of Orlicz spaces, Comment. Math., 33, 185-192 (1993) [15] Wu, C. X.; Wang, T. F.; Chen, S. T.; Wang, Y. W., Geometry of Orlicz Spaces (1987), Harbin This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.