On the uniformly normal structure of Orlicz spaces with Orlicz norm

Ting Fu Wang; Zhong Rui Shi

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 433-442
  • ISSN: 0010-2628

Abstract

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We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.

How to cite

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Wang, Ting Fu, and Shi, Zhong Rui. "On the uniformly normal structure of Orlicz spaces with Orlicz norm." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 433-442. <http://eudml.org/doc/247476>.

@article{Wang1993,
abstract = {We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.},
author = {Wang, Ting Fu, Shi, Zhong Rui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz spaces; uniformly normal structure; Orlicz spaces endowed with Orlicz norm; uniformly normal structure; reflexivity},
language = {eng},
number = {3},
pages = {433-442},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the uniformly normal structure of Orlicz spaces with Orlicz norm},
url = {http://eudml.org/doc/247476},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Wang, Ting Fu
AU - Shi, Zhong Rui
TI - On the uniformly normal structure of Orlicz spaces with Orlicz norm
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 433
EP - 442
AB - We prove that in Orlicz spaces endowed with Orlicz norm the uniformly normal structure is equivalent to the reflexivity.
LA - eng
KW - Orlicz spaces; uniformly normal structure; Orlicz spaces endowed with Orlicz norm; uniformly normal structure; reflexivity
UR - http://eudml.org/doc/247476
ER -

References

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  1. Belluce L.P., Kirk W.A., Steiner E.F., Normal structure in Banach spaces, Pacific J. Math. 26 (1968), 433-440. (1968) Zbl0164.15001MR0233178
  2. Bae J.S., Reflexivity of a Banach space with a uniformly normal structure, Proc. Amer. Math. Soc. 90 (1984), 269-270. (1984) Zbl0548.46014MR0727247
  3. Landes T., Normal structure and weakly normal structure of Orlicz sequence spaces, Trans. AMS 285 (1984), 523-533. (1984) Zbl0594.46010MR0752489
  4. Tingfu Wang, Baoxiang Wang, Normal structure ad sum-property and LD property of Orlicz spaces, J. Math. Res. Exp. 12 (1992), 477-478. (1992) 
  5. Shutao Chen, Yanzheng Duan, Normal structure and weakly normal structure of Orlicz space s, Comment. Math. Univ. Carolinae 32 (1991), 219-225. (1991) MR1137782
  6. Shutao Chen, Huiying Sun, Reflexive Orlicz spaces have uniformly normal structure, to appear. MR1269776
  7. Krasnoselskii M.A., Rutickii Ya.B., Convex Functions and Orlicz Spaces, Moscow, 1958. 
  8. Wu C., Wang T., Chen S., Wang Y., Geometry of Orlicz Spaces, H.I.T. Press, Harbin, 1986. 
  9. Shutao Chen, Some rotundities of Orlicz spaces with Orlicz norm, Bull. Polish Academy Sci. Math. 34 (1986), 585-596. (1986) MR0884206

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