Monotonicity properties of Lorentz spaces
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- by Henryk Hudzik and Anna Kamińska PDF
- Proc. Amer. Math. Soc. 123 (1995), 2715-2721 Request permission
Abstract:
Criteria for uniform monotonicity, local uniform monotonicity and strict monotonicity of Lorentz spaces are given.References
- M. A. Akcoglu and L. Sucheston, On uniform monotonicity of norms and ergodic theorems in function spaces, Proceedings of the conference commemorating the 1st centennial of the Circolo Matematico di Palermo (Italian) (Palermo, 1984), 1985, pp. 325–335. MR 881411
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- Bernard Bru and Henri Heinich, Monotonies des espaces d’Orlicz, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 19, 893–894 (French, with English summary). MR 823148
- Bernard Bru and Henri Heinich, Applications de dualité dans les espaces de Köthe, Studia Math. 93 (1989), no. 1, 41–69 (French, with English summary). MR 989567, DOI 10.4064/sm-93-1-41-69
- N. L. Carothers, Rearrangement invariant subspaces of Lorentz function spaces, Israel J. Math. 40 (1981), no. 3-4, 217–228 (1982). MR 654578, DOI 10.1007/BF02761363
- Joan Cerdà, Henryk Hudzik, and Mieczysław Mastyło, On the geometry of some Calderón-Lozanovskiĭ interpolation spaces, Indag. Math. (N.S.) 6 (1995), no. 1, 35–49. MR 1324436, DOI 10.1016/0019-3577(95)98199-L
- William J. Davis, Nassif Ghoussoub, and Joram Lindenstrauss, A lattice renorming theorem and applications to vector-valued processes, Trans. Amer. Math. Soc. 263 (1981), no. 2, 531–540. MR 594424, DOI 10.1090/S0002-9947-1981-0594424-2
- Israel Halperin, Uniform convexity in function spaces, Duke Math. J. 21 (1954), 195–204. MR 61756 H. Hudzik and W. Kurc, Monotonicity properties of Musielak-Orlicz spaces equipped with the Orlicz norm (to appear).
- Anna Kamińska, Uniform convexity of generalized Lorentz spaces, Arch. Math. (Basel) 56 (1991), no. 2, 181–188. MR 1086486, DOI 10.1007/BF01200349
- S. G. Kreĭn, Yu. Ī. Petunīn, and E. M. Semënov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, R.I., 1982. Translated from the Russian by J. Szűcs. MR 649411
- W. Kurc, Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation, J. Approx. Theory 69 (1992), no. 2, 173–187. MR 1160253, DOI 10.1016/0021-9045(92)90141-A
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9 W. A. J. Luxemburg and A. Zaanen, Riesz spaces I, North-Holland, Amsterdam and London, 1971.
- Arthur Medzhitov and Pheodor Sukochev, The property $(H)$ in Orlicz spaces, Bull. Polish Acad. Sci. Math. 40 (1992), no. 1, 5–11. MR 1402302
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2715-2721
- MSC: Primary 46E30; Secondary 46B04
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273499-7
- MathSciNet review: 1273499