On P -convex Musielak-Orlicz spaces

Paweł Kolwicz; Ryszard Płuciennik

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 4, page 655-672
  • ISSN: 0010-2628

Abstract

top
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].

How to cite

top

Kolwicz, Paweł, and Płuciennik, Ryszard. "On $P$-convex Musielak-Orlicz spaces." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 655-672. <http://eudml.org/doc/247774>.

@article{Kolwicz1995,
abstract = {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].},
author = {Kolwicz, Paweł, Płuciennik, Ryszard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Musielak-Orlicz spaces; $P$-convexity; reflexivity; Musielak-Orlicz space; reflexive; -convex},
language = {eng},
number = {4},
pages = {655-672},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $P$-convex Musielak-Orlicz spaces},
url = {http://eudml.org/doc/247774},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Kolwicz, Paweł
AU - Płuciennik, Ryszard
TI - On $P$-convex Musielak-Orlicz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 4
SP - 655
EP - 672
AB - 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].
LA - eng
KW - Musielak-Orlicz spaces; $P$-convexity; reflexivity; Musielak-Orlicz space; reflexive; -convex
UR - http://eudml.org/doc/247774
ER -

References

top
  1. Akimovic V., On uniformly convex and uniformly smooth Orlicz spaces (Russian), Teorija Funkcji Funk. Anal. i Pril. 15 (1970), 114-120. (1970) 
  2. Algherk H., Hudzik H., Uniformly non- l n 1 Musielak-Orlicz spaces of Bochner type, Forum Math. 1 (1989), 403-410. (1989) MR1016681
  3. Amir D., Franchetti C., The radius ratio and convexity properties in normed linear spaces, Trans. Amer. Math. Soc. 282 (1984), 275-291. (1984) Zbl0543.46007MR0728713
  4. Denker M., Hudzik H., Uniformly non- l n 1 Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. 101:2 (1991), 71-86. (1991) MR1125480
  5. Denker M., Kombrink R., On B -convex Orlicz spaces, Proc. Second Internat. Conf., Oberwolfach, 1978, pp. 87-95. Zbl0426.46017MR0537694
  6. Giesy D.P., On a convexity condition in normed linear spaces, Trans. Amer. Math. Soc. 125 (1966), 114-146. (1966) MR0205031
  7. Hudzik H., Kamińska A., On uniformly convexifiable and B -convex Musielak-Orlicz spaces, Commentat. Math. 25 (1985), 59-75. (1985) MR0795121
  8. 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) MR0939005
  9. James R.C., Uniformly non-square Banach spaces, Ann. of Math. 2 80 (1964), 542-550. (1964) Zbl0132.08902MR0173932
  10. James R.C., A nonreflexive Banach space that is uniformly nonoctahedral, Israel J. Math. 18 (1974), 145-155. (1974) Zbl0292.46014MR0355538
  11. Kamińska A., Some convexity properties of Musielak-Orlicz spaces of Bochner type, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Proc. of the 13 Winter School on Abstract Analysis, Ser. II. 10 (1985), 63-73. MR0894273
  12. Kottman C.A., Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565-576. (1970) Zbl0208.37503MR0265918
  13. Milman D., On some criteria for the regularity of spaces of type (B) (Russian), Doklady Akad. Nauk SSSR 20 (1938). (1938) 
  14. Musielak J., Orlicz spaces and modular spaces, Lecture Notes in Math. 1034 (1983), 1-222. (1983) Zbl0557.46020MR0724434
  15. Sastry K.P.R., Naidu S.V.R., Convexity conditions in normed linear spaces, J. Reine Angew. Math. 297 (1978), 35-53. (1978) Zbl0364.46009MR0493265
  16. Ye Yining, He Miaohong, Płuciennik R., P -convexity and reflexivity of Orlicz spaces, Comment. Math. 31 (1991), 203-216. (1991) 
  17. Ye Yining, Huang Yafeng, P -convexity property in Musielak-Orlicz sequence spaces, Collect. Math. 44 (1993), 307-325. (1993) Zbl0816.46004MR1280747
  18. Ye Yining, Li Yanhong, Reflexivity conditions for an Orlicz spaces (Chinese), North-East Math. 2 (3), (1986), 309-323. (1986) MR0889565

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.