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On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm

Published online by Cambridge University Press:  20 November 2018

Yaqiang Yan
Yaqiang Yan*
Affiliation:
Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China, e-mail: yanyq@pub.sz.jsinfo.net
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Abstract

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Let ${{l}^{\Phi }}$ and ${{L}^{\Phi }}\left( \Omega \right)$ be the Orlicz sequence space and function space generated by $N$-function $\Phi (u)$ with Orlicz norm. We give equivalent expressions for the nonsquare constants ${{C}_{J}}\left( {{l}^{\Phi }} \right),\,{{C}_{J}}\left( {{L}^{\Phi }}\left( \Omega \right) \right)$ in sense of James and ${{C}_{S}}\left( {{l}^{\Phi }} \right),\,{{C}_{S}}\left( {{L}^{\Phi }}\left( \Omega \right) \right)$ in sense of Schäffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces ${{l}^{\Phi }}$ and ${{L}^{\Phi}}\left(\Omega \right)$.

Keywords

46E30James nonsquare constantSchäffer nonsquare constantOrlicz sequence spaceOrlicz function space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 1 , 01 February 2003 , pp. 204 - 224
Copyright
Copyright © Canadian Mathematical Society 2003

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