Abstract
We discuss Orlicz spaces with uniform λ-property. These spaces are equipped with the Orlicz norm and they are generated by arbitrary Orlicz functions (even Orlicz functions which vanish outside zero and which attain infinite values to the right of some point u > 0 are not excluded).
References
- R. M. Aron, R. H. Lohman: A geometric function determined by extreme points of the unit ball of a normed space, Pacific J. Math. 127 (1987) 209–231.https://doi.org/10.2140/pjm.1987.127.209Google Scholar
- R. M. Aron, R. H. Lohman, A. Suárez Granero: Rotundity, the C.S.R.P., and the λ-property in Banach spaces, Proc. Amer. Math. Soc. 111 (1991) 151–155.https://doi.org/10.1090/S0002-9939-1991-1030732-0Google Scholar
- C. Benett, R. Sharpley: Interpolation of Operators, Academic Press, London (1988).Google Scholar
- A. Bohonos, R. Płuciennik: λ-property in Orlicz spaces, J. Convex Analysis 21/1 (2014) 147–166.https://doi.org/10.68381/jca21007Google Scholar
- A. Bohonos, R. Płuciennik: Uniform λ-property in L1 ∩ L∞, Comm. Mathematicae 55/2 (2015) 171–181.https://doi.org/10.14708/cm.v55i2.1122Google Scholar
- S. T. Chen: Geometry of Orlicz Spaces, Dissertations in Mathematics 356, Polish Academy of Sciences, Warsaw (1996).Google Scholar
- S. T. Chen, H. Y. Sun, C. X. Wu: λ-property of Orlicz spaces, Bull. Acad. Polon. Sci. Math. 39/1-2 (1991) 63–69.Google Scholar
- M. Ciesielski: On geometric structure of symmetric spaces, J. Math. Anal. Appl. 426/2 (2015) 700–726.https://doi.org/10.1016/j.jmaa.2015.01.064Google Scholar
- M. Ciesielski, P. Kolwicz, R. Płuciennik: Local approach to Kadec-Klee properties in symmetric function spaces, J. Math. Anal. Appl. 426/2 (2015) 700–726.https://doi.org/10.1016/j.jmaa.2015.01.064Google Scholar
- J. A. Clarkson: Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936) 396–414.https://doi.org/10.1090/S0002-9947-1936-1501880-4Google Scholar
- Y. Cui, L. Duan, H. Hudzik, M. Wisła: Basic theory of p-Amemiya norm in Orlicz spaces (1 ≤ p ≤ 1) : Extreme points and rotundity in Orlicz spaces equipped with these norms, Nonlinear Analysis 69 (2008) 1796–1816.https://doi.org/10.1016/j.na.2007.07.026Google Scholar
- Y. A. Cui, H. Hudzik, R. Płuciennik: Extreme points and strongly extreme points in Orlicz spaces equipped with the Orlicz norm, Z. Analysis Anwendungen 22/4 (2003) 789–817.https://doi.org/10.4171/zaa/1174Google Scholar
- J. Diestel: Sequences and Series in Banach Spaces, Graduate Texts in Mathematics 92, Springer, New York (1984).https://doi.org/10.1007/978-1-4612-5200-9Google Scholar
- P. Foralewski, H. Hudzik, R. Płuciennik: Orlicz spaces without extreme points, J. Math. Anal. Appl. 361 (2010) 506–519.https://doi.org/10.1016/j.jmaa.2009.07.015Google Scholar
- A. S. Granero: λ-property in Orlicz spaces, Bull. Acad. Polon. Sci. Math. 37/7-12 (1989) 421–431.Google Scholar
- H. Hudzik, L. Maligranda: Amemiya norm equals Orlicz norm in general, Indag. Math. (N.S.) 11/4 (2000) 573–585.https://doi.org/10.1016/S0019-3577(00)80026-9Google Scholar
- R. H. Lohman: The λ-function in Banach spaces, in: Banach Space Theory, Contemporary Mathematics 85, American Mathematical Society, Providence (1989) 345–351.https://doi.org/10.1090/conm/085/983393Google Scholar
- J. Musielak: Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034, Springer, Berlin (1983).https://doi.org/10.1007/BFb0072210Google Scholar
- M. M. Rao, Z. D. Ren: Theory of Orlicz Spaces, Marcel Dekker, New York (1991).Google Scholar
- H. Y. Sun, C. X. Wu: λ-property of Orlicz space LM, Comm. Math. Univ. Carolinae 31 (1990) 731–741.Google Scholar
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