Abstract
We start with some results concerning ULUM and UM points in general Köthe sequence spaces. Next we present full characterization of ULUM points in Calderón-Lozanovskii spaces. In particular, we obtain the respective criteria for ULUM points in Orlicz-Lorentz spaces and Orlicz spaces.
References
- M. A. Akcoglu, L. Sucheston: On uniform monotonicity of norms and ergodic theorems in function spaces, Rend. Circ. Mat. Palermo, II. Ser., Suppl. 8 (1985) 325–335.Google Scholar
- C. Bennett, R. Sharpley: Interpolation of Operators, Academic Press, Boston (1988).Google Scholar
- G. Birkhoff: Lattice Theory, 3rd Ed., AMS, Providence (1967).Google Scholar
- J. Cerdá, H. Hudzik, A. Kamińska, M. Mastyło: Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces, Positivity 2 (1998) 311–337.https://doi.org/10.1023/A:1009728519669Google Scholar
- J. Cerdá, H. Hudzik, M. Mastyło: On the geometry of some Calderón-Lozanovskiĭ interpolation spaces, Indag. Math., New Ser. 6(1) (1995) 35–49.https://doi.org/10.1016/0019-3577(95)98199-LGoogle Scholar
- I. Dobrakov: On submeasures. I, Dissertationes Math., Warszawa (1974).Google Scholar
- P. Foralewski, H. Hudzik: On some geometric properties of generalized Calderón-Lozanovskiĭ sequence spaces, Acta Math. Hung. 80(1–2) (1998) 55–66.https://doi.org/10.1023/A:1006516607913Google Scholar
- P. Foralewski, H. Hudzik: Some basic properties of generalized Calderón-Lozanovskiĭ spaces, Collect. Math. 48(4–6) (1997) 523–538.Google Scholar
- P. Foralewski, H. Hudzik: On some geometrical and topological properties of generalized Calderón-Lozanovskiĭ sequence spaces, Houston J. Math. 25(3) (1999) 523–542.Google Scholar
- P. Foralewski, P. Kolwicz: Local uniform rotundity in Calderón-Lozanovskiĭ spaces, J. Convex Analysis 14(2) (2007) 395–412.https://doi.org/10.68381/jca14026Google Scholar
- H. Hudzik, A. Kamińska: Monotonicity properties of Lorentz spaces, Proc. Amer. Math. Soc. 123(9) (1995) 2715–2721.https://doi.org/10.1090/S0002-9939-1995-1273499-7Google Scholar
- H. Hudzik, A. Kamińska, M. Mastyło: Geometric properties of some Calderón-Lozanovskiĭ spaces and Orlicz-Lorentz spaces, Houston J. Math. 22 (1996) 639–663.Google Scholar
- H. Hudzik, A. Kamińska, M. Mastyło: On geometric properties of Orlicz-Lorentz spaces, Can. Math. Bull. 40(3) (1997) 316–329.https://doi.org/10.4153/CMB-1997-038-6Google Scholar
- H. Hudzik, A. Kamińska, M. Mastyło: Monotonicity and rotundity properties in Banach lattices, Rocky Mt. J. Math. 30(3) (2000) 933–949.https://doi.org/10.1216/rmjm/1021477253Google Scholar
- H. Hudzik, P. Kolwicz, A. Narloch: Local rotundity structure of Calderón-Lozanovskiĭ spaces, Indag. Math., New Ser. 17(3) (2006) 373–395.https://doi.org/10.1016/S0019-3577(06)80039-XGoogle Scholar
- H. Hudzik, W. Kurc: Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices, J. Approximation Theory 95 (1998) 353–368.https://doi.org/10.1006/jath.1997.3226Google Scholar
- H. Hudzik, X. Liu, T. Wang: Points of monotonicity in Musielak-Orlicz function spaces endowed with the Luxemburg norm, Arch. Math. 82(6) (2004) 534–545.https://doi.org/10.1007/s00013-003-0440-xGoogle Scholar
- H. Hudzik, A. Narloch: Local monotonicity structure of Calderón-Lozanovskiĭ spaces, Indag. Math., New Ser. 15(1) (2004) 1–12.https://doi.org/10.1016/S0019-3577(04)90017-1Google Scholar
- A. Kamińska: Some remarks on Orlicz-Lorentz spaces, Math. Nachr. 147 (1990) 29–38.https://doi.org/10.1002/mana.19901470104Google Scholar
- A. Kamińska: Uniform convexity of generalized Lorentz spaces, Arch. Math. 56 (1991) 181–188.https://doi.org/10.1007/BF01200349Google Scholar
- L. V. Kantorovich, G. P. Akilov: Functional Analysis, 3rd Ed., Nauka, Moscow (1984), (in Russian).Google Scholar
- P. Kolwicz: Rotundity properties in Calderó n-Lozanovskiĭ spaces, Houston J. Math. 31(3) (2005) 883–912.Google Scholar
- P. Kolwicz, R. Płuciennik: On uniform rotundity in every direction in Calderón-Lozanovskiĭ sequence spaces, J. Convex Analysis 14(3) (2007) 621–645.https://doi.org/10.68381/jca14037Google Scholar
- P. Kolwicz, R. Płuciennik: Local ∆2 (x) condition as a crucial tool for local structure of Calderón-Lozanovskiĭ sequence spaces, J. Math. Anal. Appl. 356(2) (2009) 605–614.https://doi.org/10.1016/j.jmaa.2009.03.030Google Scholar
- S. G. Krein, Yu. I. Petunin, E. M. Semenov: Interpolation of Linear Operators, Nauka, Moscow (1978), (in Russian).Google Scholar
- W. Kurc: Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation, J. Approximation Theory 69(2) (1992) 173–187.https://doi.org/10.1016/0021-9045(92)90141-AGoogle Scholar
- J. Lindenstrauss, L. Tzafriri: Classical Banach spaces. II: Function Spaces, Springer, Berlin (1979).https://doi.org/10.1007/978-3-662-35347-9Google Scholar
- W. A. J. Luxemburg: Banach Function Spaces, Van Gorcum, Assen (1955).https://doi.org/10.1016/S1385-7258(56)50016-9Google Scholar
- W. A. J. Luxemburg: Rearrangement invariant Banach function spaces, in: Symposium in Analysis (Kingston / Canada, 1967), Queen’s Papers in Pure and Applied Mathematics 10, Queen’s University, Kingston / Canada (1967) 83–144.Google Scholar
- W. Wnuk: Banach Lattices with Order Continuous Norms, Polish Scientific Publishers PWN, Warszawa (1999).Google Scholar
Suggested citation
Published by Heldermann Verlag, 2010. Rights now held by Banach Press LLC.
