Taiwanese Journal of Mathematics

EXPOSED POINTS AND STRONGLY EXPOSED POINTS IN MUSIELAK-ORLICZ SEQUENCE SPACES

Zhongrui Shi and Chunyan Liu

Full-text: Open access

Abstract

In this paper we give criteria of exposed points and strongly exposed points in Musielak-Orlicz sequence spaces endowed with Luxemburg norm.

Article information

Source
Taiwanese J. Math., Volume 16, Number 1 (2012), 305-322.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406542

Digital Object Identifier
doi:10.11650/twjm/1500406542

Mathematical Reviews number (MathSciNet)
MR2887866

Zentralblatt MATH identifier
1242.46020

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Musielak-Orlicz sequence spaces Luxemburg norm exposed points strongly exposed points

Citation

Shi, Zhongrui; Liu, Chunyan. EXPOSED POINTS AND STRONGLY EXPOSED POINTS IN MUSIELAK-ORLICZ SEQUENCE SPACES. Taiwanese J. Math. 16 (2012), no. 1, 305--322. doi:10.11650/twjm/1500406542. https://projecteuclid.org/euclid.twjm/1500406542


Export citation

References

  • B. Wang, Exposed points of Orlicz spaces, Journal of Baoji Teacher College $($Scince$)$, 12(2) (1989), 43-49.
  • M. Li, B. Wang and T. Wang, Strongly exposed points of Orlicz sequence spaces, Acta Mathematica Sinica, 42(4) (1999), 645-648.
  • T. Wang, D. Ji and Z. Shi, The criteria of strongly exposed points in Orlicz spaces, Comment. Math. Univ. Carolin., 35(4) (1994), 721-724.
  • L. Zhao and Y. Cui, Exposed points in Musielak-Orlicz sequence space endowed with the Luxemburg norm, Natur. Sci. J. Harbin Normal Univ., 12(4) (2005), 3-6.
  • S. Straszewicz, $\ddot{U}$ber exponierte punkte abgeschlossener punktmengen, Fund. Math., 24 (1935), 139-143.
  • J. Lindenstranss, On oprators which attain their norm, Israel J. Math., 1 (1963), 139-148.
  • H. Hudzik and Y. Ye, Support functional and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm, Comment. Math. Univ. Carolin., 31(4) (1990), 661-684.
  • M. A. Krasnoselskii and Ya. B. Rutickii, Convex function and Orlicz spaces, Groningen, 1961.
  • S. Chen, Geometry of Orlicz spaces, Dissertationes Mathematicae, 356, Warszawa, 1996.
  • J. Musielak, Orlicz spaces and modular spaces, in: Lecture Notes in Math., Vol. 1034, Springer-Verlag, 1983.
  • M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker Inc., 1991.
  • Z. Shi and R. Zhang, On smoothness of Orlicz-Musielak sequence spaces, J. Mathematics, 19(4) (1999), 354-360.
  • L. Cao and T. Wang, Some notes about $K(x)\neq\phi$ in Musielak-Orlicz spaces, Natur. Sci. J. Harbin Normal Univ., 16(4) (2000), 1-4.
  • M. Zuo, Y. Cui and H. Hudzik, On the points of local uniform rotundity and weak local uniform rotundity in Musielak-Orlicz sequence spaces equipped with the Orlicz norm, Nonlinear Analysis, 71 (2009), 4906-4915.
  • X. Liu and T. Wang, Extreme points and strongly extreme points of Musielak-Orlicz sequence spaces, Acta Mathematica Sinica $($English Series$)$, 21(2) (2005), 267-268.
  • T. Wang and S. Bian, Smooth points and strongly (very) smooth points of Musielak-Orlicz spaces with Orlicz norm, Acta Analysis Functionals Applicata, 1(1) (1999), 61-68.
  • A. Kaminska, Rotundity of Orlicz-Musielak Sequence spaces, Bull. Polish. Acad. Sci, Math., 29 (1981), 137-144.