Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Isometric copies of $l^1$ and $l^{\infty}$ in Orlicz spaces equipped with the Orlicz norm


Authors: Shutao Chen, Yunan Cui and Henryk Hudzik
Journal: Proc. Amer. Math. Soc. 132 (2004), 473-480
MSC (2000): Primary 46B20, 46E30
DOI: https://doi.org/10.1090/S0002-9939-03-07099-0
Published electronically: July 2, 2003
MathSciNet review: 2022371
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of $l^1$ (or $l^{\infty}$) are given.


References [Enhancements On Off] (What's this?)

  • 1. S. T. Chen, Geometry of Orlicz Spaces, Dissertationes Math. 356 (1996), 1-204. MR 97i:46051
  • 2. Y. A. Cui, H. Hudzik, M. Nowak and R. P\luciennik, Some geometric properties in Orlicz sequence spaces equipped with the Orlicz norm, J. Convex Analysis 6(1) (1999), 91-113. MR 2000j:46037
  • 3. R. Grzaslewicz and H. Hudzik, Smooth points of Orlicz spaces equipped with Luxemburg norm, Math. Nachr. 155 (1992), 31-45. MR 94k:46057
  • 4. H. Hudzik, Banach lattices with order isomertric copies of $l^{\infty}$, Indag. Math. 9 (4) (1998), 521-527. MR 2000d:46025
  • 5. H. Hudzik and W. Kurc, Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices, J. Approx. Theory 95 (1998), 353-368. MR 99k:46044
  • 6. H. Hudzik and L. Maligranda, Amemiya norm equals Orlicz norm in general, Indag. Mathem. 11 (4) (2000), 573-585.
  • 7. A. Kaminska, Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Math. 30 (1982), no. 7-8, 347-352. MR 84h:46013
  • 8. M. A. Krasnoselskii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, P. Noordhoff Ltd., Groningen 1961 (translation). MR 23:A4016
  • 9. W. A. J. Luxemburg, Banach Function Spaces, Thesis, Technische Hogeschoolte Delft, 1955. MR 17:285a
  • 10. L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math. 5, Univ. Estadual de Campinas, Campinas, SP, Brasil 1989.
  • 11. J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983. MR 85m:46028
  • 12. M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, Inc., New York, Basel, Hong Kong, 1991. MR 92e:46059
  • 13. M. Wis\la, On a class of Orlicz sequence spaces isomorphic to $l^{\infty}$, to appear.
  • 14. M. Wójtowicz, Contractive projections onto isometric copies of $L^1(\nu)$ in strictly monotone Banach lattices, to appear.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20, 46E30

Retrieve articles in all journals with MSC (2000): 46B20, 46E30


Additional Information

Shutao Chen
Affiliation: Department of Mathematics, Harbin Normal University, Harbin, People’s Republic of China
Email: schen@public.hr.hl.cn

Yunan Cui
Affiliation: Department of Mathematics, Harbin University of Science and Technology, Harbin, People’s Republic of China
Email: cuiya@yahoo.com

Henryk Hudzik
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Email: hudzik@amu.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-03-07099-0
Keywords: Orlicz space, Orlicz norm, order linearly isometric copy of $l^1$, linearly isometric copy of $l^1$, order linearly isometric copy of $l^{\infty}$.
Received by editor(s): February 26, 2002
Received by editor(s) in revised form: March 20, 2002, and October 8, 2002
Published electronically: July 2, 2003
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society

American Mathematical Society