Reflexive Orlicz spaces have uniformly normal structure

Shutao Chen; Huiying Sun

Studia Mathematica (1994)

  • Volume: 109, Issue: 2, page 197-208
  • ISSN: 0039-3223

Abstract

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We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.

How to cite

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Chen, Shutao, and Sun, Huiying. "Reflexive Orlicz spaces have uniformly normal structure." Studia Mathematica 109.2 (1994): 197-208. <http://eudml.org/doc/216069>.

@article{Chen1994,
abstract = {We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.},
author = {Chen, Shutao, Sun, Huiying},
journal = {Studia Mathematica},
keywords = {Orlicz space equipped with the Luxemburg norm; uniformly normal structure; reflexive},
language = {eng},
number = {2},
pages = {197-208},
title = {Reflexive Orlicz spaces have uniformly normal structure},
url = {http://eudml.org/doc/216069},
volume = {109},
year = {1994},
}

TY - JOUR
AU - Chen, Shutao
AU - Sun, Huiying
TI - Reflexive Orlicz spaces have uniformly normal structure
JO - Studia Mathematica
PY - 1994
VL - 109
IS - 2
SP - 197
EP - 208
AB - We prove that an Orlicz space equipped with the Luxemburg norm has uniformly normal structure if and only if it is reflexive.
LA - eng
KW - Orlicz space equipped with the Luxemburg norm; uniformly normal structure; reflexive
UR - http://eudml.org/doc/216069
ER -

References

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  1. [1] J. S. Bae, Reflexivity of a Banach space with a uniformly normal structure, Proc. Amer. Math. Soc. 90 (1984), 269-270. Zbl0548.46014
  2. [2] L. P. Belluce, W. A. Kirc and E. F. Steiner, Normal structure in Banach spaces, Pacific J. Math. 26 (1968), 433-440. Zbl0164.15001
  3. [3] E. Casini and E. Maluta, Fixed point of uniformly Lipschitzian mapping in spaces with uniformly normal structure, Nonlinear Anal. 104 (1984), 285-292. 
  4. [4] S. Chen and Y. Duan, Normal structure and weakly normal structure of Orlicz spaces, Comment. Math. Univ. Carolinae 32 (1991), 219-225. Zbl0760.46023
  5. [5] A. Kamińska, On uniform convexity of Orlicz spaces, Indag. Math. 44 (1982), 27-36. Zbl0489.46025
  6. [6] M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ, Convex Functions and Orlicz Spaces, Nauka, Moscow, 1958 (in Russian). 
  7. [7] T. Landes, Normal structure and weakly normal structure of Orlicz sequence spaces, Trans. Amer. Math. Soc. 285 (1981), 523-533. Zbl0594.46010
  8. [8] S. Wang, Differentiability of Carathéodory operators, Sci. Bull. Math. 25 (1980), 42-45. 
  9. [9] T. Wang and B. Wang, Normal structure and sum-property of Orlicz sequence spaces, Chinese Math. Research & Exposition 12 (3) (1992). 
  10. [10] C. Wu, T. Wang, S. Chen and Y. Wang, Geometrical Theory of Orlicz Spaces, Harbin Inst. of Tech. Press, 1986 (in Chinese). 

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