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On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm
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- Journal:
- Canadian Journal of Mathematics / Volume 55 / Issue 1 / 01 February 2003
- Published online by Cambridge University Press:
- 20 November 2018, pp. 204-224
- Print publication:
- 01 February 2003
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- Article
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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 ${{L}^{\Phi}}\left(\Omega \right)$.
