Previous |  Up |  Next

Article

Keywords:
Musielak--Orlicz space; rotundity
Summary:
We give necessary and sufficient conditions for weak uniform rotundity of Mu\-sie\-lak--Orlicz spaces $L_\varphi $ with the Luxemburg norm. The result is a generalization of a theorem by Kami'nska and Kurc.
References:
[1] Diestel J.: Geometry of Banach spaces-selected topics. Springer Lecture Notes in Mathematics, vol. 485, 1983. MR 0461094 | Zbl 0466.46021
[2] Hudzik H.: On some equivalent conditions in Musielak-Orlicz spaces. Comment. Math. 24 (1984), 57-64. MR 0759055 | Zbl 0564.46022
[3] Hudzik H.: Strict convexity of Musielak-Orlicz spaces with Luxemburg's norm. Bull. Acad. Polon. Sci., Sér. Sci. Math., Astronom. et Phys. 29 (1981), 235-247. MR 0640468 | Zbl 0479.46014
[4] Hudzik H.: Uniform convexity of Musielak-Orlicz spaces with Luxemburg's norm. Comment. Math. 23 (1983), 21-32. MR 0709167 | Zbl 0595.46027
[5] Kamińska A.: On some convexity properties of Musielak-Orlicz spaces. Supplemento ai Rendicoti del Circolo Matematico di Palermo, The 12th Winter School on Abstract Analysis, Srní 1984. MR 0781940
[6] Kamińska A.: Weak uniform rotundity in Orlicz spaces. Comment. Math. Univ. Carolinae 27 (1986), 651-664. MR 0874658
[7] Musielak J.: Orlicz spaces and modular spaces. Springer Lecture Notes in Mathematics, vol. 1034, 1983. MR 0724434 | Zbl 0557.46020
Partner of
EuDML logo