On $P$-convex Musielak-Orlicz spaces
Kolwicz, Paweł ; Płuciennik, Ryszard
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 655-672 / Harvested from Czech Digital Mathematics Library

In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is $P$-convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].

Publié le : 1995-01-01
Classification:  46A80,  46B10,  46B20,  46E30,  46E40
@article{118794,
     author = {Pawe\l\ Kolwicz and Ryszard P\l uciennik},
     title = {On $P$-convex Musielak-Orlicz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {655-672},
     zbl = {0838.46022},
     mrnumber = {1378688},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118794}
}
Kolwicz, Paweł; Płuciennik, Ryszard. On $P$-convex Musielak-Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 655-672. http://gdmltest.u-ga.fr/item/118794/

Akimovic V. On uniformly convex and uniformly smooth Orlicz spaces (Russian), Teorija Funkcji Funk. Anal. i Pril. 15 (1970), 114-120. (1970)

Algherk H.; Hudzik H. Uniformly non-$l_n^1 $ Musielak-Orlicz spaces of Bochner type, Forum Math. 1 (1989), 403-410. (1989) | MR 1016681

Amir D.; Franchetti C. The radius ratio and convexity properties in normed linear spaces, Trans. Amer. Math. Soc. 282 (1984), 275-291. (1984) | MR 0728713 | Zbl 0543.46007

Denker M.; Hudzik H. Uniformly non-$l_n^1 $ Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. 101:2 (1991), 71-86. (1991) | MR 1125480

Denker M.; Kombrink R. On $B$-convex Orlicz spaces, Proc. Second Internat. Conf., Oberwolfach, 1978, pp. 87-95. | MR 0537694 | Zbl 0426.46017

Giesy D.P. On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114-146. (1966) | MR 0205031

Hudzik H.; Kamińska A. On uniformly convexifiable and $B$-convex Musielak-Orlicz spaces, Commentat. Math. 25 (1985), 59-75. (1985) | MR 0795121

Hudzik H.; Kamińska A.; Kurc W. Uniformly non-$l_n^1 $ Musielak-Orlicz spaces, Bull. Acad. Polon. Sci. Math. 35 no. 7-8 (1987), 441-448. (1987) | MR 0939005

James R.C. Uniformly non-square Banach spaces, Ann. of Math. 2 80 (1964), 542-550. (1964) | MR 0173932 | Zbl 0132.08902

James R.C. A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145-155. (1974) | MR 0355538 | Zbl 0292.46014

Kamińska A. Some convexity properties of Musielak-Orlicz spaces of Bochner type, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Proc. of the 13$^{th}$ Winter School on Abstract Analysis, Ser. II. 10 (1985), 63-73. | MR 0894273

Kottman C.A. Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565-576. (1970) | MR 0265918 | Zbl 0208.37503

Milman D. On some criteria for the regularity of spaces of type (B) (Russian), Doklady Akad. Nauk SSSR 20 (1938). (1938)

Musielak J. Orlicz spaces and modular spaces, Lecture Notes in Math. 1034 (1983), 1-222. (1983) | MR 0724434 | Zbl 0557.46020

Sastry K.P.R.; Naidu S.V.R. Convexity conditions in normed linear spaces, J. Reine Angew. Math. 297 (1978), 35-53. (1978) | MR 0493265 | Zbl 0364.46009

Ye Yining; He Miaohong; Płuciennik R. $P$-convexity and reflexivity of Orlicz spaces, Comment. Math. 31 (1991), 203-216. (1991)

Ye Yining; Huang Yafeng $P$-convexity property in Musielak-Orlicz sequence spaces, Collect. Math. 44 (1993), 307-325. (1993) | MR 1280747 | Zbl 0816.46004

Ye Yining; Li Yanhong Reflexivity conditions for an Orlicz spaces (Chinese), North-East Math. 2 (3), (1986), 309-323. (1986) | MR 0889565