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Proceedings of the American Mathematical Society
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
Published electronically: July 2, 2003
MathSciNet review: 2022371
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-03-07099-0
PII: S 0002-9939(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